It is unlikely that Zachariah, the Prophet (AS), might have prayed to God to grant him a child who would inherit him. Hence, why did Lady Fatima Zahra (SA) demand inheritance relying on this verse?
question
Salamun alaikum, Some Sunni scholars argue that divine prophets left no inheritance for their offspring and descendants. Therefore, as per their saying, Fatima Zahra\'s argument relying on Prophet Yahya\'s inheritance for Zachariah or that of Sulayman for Dawood is not acceptable and cannot be a credible argument to prove Fatima\'s right to inheritance. They present the following arguments: 1. It is not befitting even for a believing man to pray to God to grant him a child to inherit him, much less Prophet Zachariah or other prophets. 2. Based on the widely-known report, Zachariah was a poor man who adopted carpentry as his profession. What did he have of worldly things to pray to God to grant him a (male) child to inherit him? The general principle about divine prophets is that prophets do not store any wealth or property and whatever they have are spent in the way of Allah, not to mention the fact that Prophet Yahya died before Prophet Zachariah! 3. The word "inheritance" (irth) is not applicable to inheriting properties only; it is rather applicable to knowledge, prophethood, sultanate, etc. in the sense that these can also be inherited. 4. There is a narration that religious scholars are heirs to prophets and the prophets do not leave behind any dirham and dinar. What they leave for their heirs is knowledge. Having said that, how can this argument be rejected? How can we prove that the term \'inheritance\' does not refer to property or material wealth? Thanks Muhammad Meftah
Concise answer
Some of the verses to which Lady Fatima (SA) made reference to prove her right and ownership of Fadak, are related to material inheritance and some others are general and they seem to be more consistent with spiritual inheritance but material inheritance also cannot be excluded. Yet, the main point in her argument is that every child inherits his or her father according to the Quran and that there is no verse to indicate that prophet's children do not inherit their parents. Is there one such verse?
Naturally, the fact that some individuals – especially those who chanted the slogan "The Book of Allah suffices us" through which they attained power — are referring to a tradition from the Prophet (S) in this regard cannot be an appropriate answer to this strong and powerful argument by the Holy Prophet's daughter, peace be upon them.

Detailed Answer
This question might, at first glance, seem to be logical and sensible and some have, with this literalist perspective, endeavored to criticize Lady Zahra's (S) argument with reliance on the basis of verses to prove her ownership of the land of Fadak. Naturally, to study this historical event thoroughly, we need to briefly analyze relevant subject matters to come to a precise conclusion in this regard:
First subject: The fact that Fadak was among the properties obtained without bloodshed and war and it was under the disposal of Prophet Muhammad (S) is something that cannot be denied because there are historical proofs showing that it belonged to the Prophet (S). Moreover, the exegetes of the Holy Quran also consider Fadak to be one of the main manifestations of the verse revealed in this regard.[1] On the other hand, it was natural that properties which belonged to Prophet (S) be inherited by his heirs. Given the fact that Fatima Zahra (SA) was the Prophet's only child, she would inherit a major part of her father's property and a very small part of it would be inherited by his wives.
Second subject: Shiites believe that the land of Fadak was gifted to Fatima Zahra during the Prophet's lifetime. However, it did not make any difference whether it was gifted during his lifetime or inherited even after the demise of the Prophet (S) because if it had been gifted to Fatima (SA), there is no question of inheritance and if it had not been gifted, it could have been inherited by her by way of the law of inheritance.
Third subject: Based on what has been clearly and explicitly stated in Sunni sources, the Prophet (S) wanted to write a will at the time of his death but the second caliph prevented him from writing one by saying "the Book of Allah suffices us". Indeed, he cleverly declared that he did not consider anything other than the Quran to be valid or binding.[2] This action was taken on the part of a circle which finally managed to take the caliphate out of the family of the Prophet, peace be upon him and his family.
Naturally, following this incident it was now the time to deprive the family of the Prophet (S) of everything that could be a financial source for them as it happened in practice.
This was a decision that was made and the way it had to be implemented was on the next phase of action. In doing so, it did not make any difference for those who wanted to implement this decision whether Fadak had been gifted to Fatima or it was inherited. Most likely, they had a premeditated plan for both.
Fourth subject: Now that the conditions and circumstances had developed in such a way and to such a degree that it was not possible to restore the right through its natural and legal course of action, it was necessary that the course of action that was going to be adopted was to be one that would make it easier for truth seekers to pass judgment in future. In line with this objective, the daughter of the Holy Prophet (S) embarked on a strategy to restore her right presenting an argument to which the opponent had no answer to give or they resorted to justifications which were precisely against their earlier approaches. This method of argument in the history of the Ahlulbayt (AS) has other manifestations which, for instance, have been discussed in question 11206 (on our website).
To explain further, had Lady Fatima Zahra, peace be upon her, said that Fadak had been gifted to her, then the opponents would tell her to present witnesses to prove her claim. On the other hand, informed people would be pressured to avoid giving testimony. Even if someone would presumably dare to give testimony in her favor, the opponents would falsify him or would consider the testimony as insufficient. Thus, efforts were made to proclaim that the land of Fadak had never been proven to have been gifted to Fatima by her father, the Prophet, peace be upon him and his family. That was why Fatima Zahra (SA) did not so often claim that the land had been gifted to her. In fact, she followed another course of action and that was to argue that the land was a property of her father and she was entitled to it as a heir. That was because all Muslims knew that Fadak was at the disposal of Prophet Muhammad (S) and it was so widely known amongst Muslims that it did not require any witnesses. The fact that the land was under the disposal of the Prophet (S) was not even denied by the opponents. Fatima Zahra (SA) said that the land had been inherited by her. That is to say, even if the land had not been gifted, she got it through inheritance. That is why she demanded what she believed to have inherited from her father.
To prove herself as the heir to the Prophet (S), Fatima (SA) did not resort to any sayings of her father but she made reference to a number of verses from the Holy Quran some of which directly and clearly related to inheritance[3] and some others could include both spiritual and material inheritance.[4] However, the most important points derived from her arguments were the following:
A) The subject of inheritance has been principally mentioned by the Quran and it is accepted by all Muslims. Given that the Quran is the most trusted source of legislation and the opponents considered the Quran as the only credible source[5], there is no verse in the Quran to state that the prophets' children are deprived from inheritances. If there is one such verse, where is it and in which Surah of the Quran is it?
B) Assuming that some of the verses of the Quran imply spiritual inheritance, how can we prove that such verses never include material inheritance?
C) You (the opponents) prevented my father from writing a will with the motto that "God's Book is sufficient for us", now you should answer me with reliance on the same Book that I cannot inherit my father. Do not speak of my father's saying (hadith) since you have violated his advice and instructions more than anyone else.
With that said, we will now review parts of this historic story with reliance on two of the most reliable and most trusted Sunni sources:
A) Fatima Zahra (SA) criticized her opponents by saying: "Do you leave God's book and its teachings aside to confiscate the Prophet's property? God says in the Quran:
1. Sulayman inherited Dawood.
2. So grant me from you a successor to inherit me, and to inherit the family of Jacob (story of Yahya and Zachariah).
3. Based on God's commandment, some of the members of the family are more entitled to others in terms of receiving inheritance.
4. God advised you to give your sons inheritance double of the share of your daughters.
5. It is the duty of the virtuous and God-fearing men and women that if they are going to leave anything to be inherited by their heirs, they should leave necessary recommendations about how their father, mother and near relatives should use their property.
With all these verses in the Quran, do you think I have no right to my father's property and I do not inherit him as though I have no relationship with him?
Is there a verse in the Quran about inheritance that is particular to you and in which God might have excluded the Prophet (S), or otherwise you are saying that we are from two different religions and it is for the same reason that we do not inherit?! Weren't I and my father from the same religion? Perhaps, you might be thinking that you are understanding the Quran better the Prophet (S)?
Are you looking forward to seeing the law of the era of ignorance back in society?
Am I becoming deprived of inheritance due to injustice and repression?
Verily, the oppressors shall know what fate awaits them![6]
B) Fatima Zahra (SA), Imam Ali (AS) and Abbas, the Prophet's uncle went to Abu Bakr and demanded inheritance. Addressing them, Abu Bakr said: "We [the prophets] do not leave any inheritance behind, and what we leave behind is charity and the expenses which the Prophet (S) undertook, I will too undertake it."
Imam Ali (AS) said: "Sulayman inherited Davood and Zachariah prayed to God to be granted a child who would inherit him and the family of Prophet Jacob."
Abu Bakr said: "What I am saying is true. By God, you know what I know."
Imam Ali said: "This is the book of God which speaks clearly and frankly."
After this talk, silence prevailed and everybody got back to his respective place.[7]
C) It has been narrated from the second caliph that the day the Prophet (S) departed, he took allegiance for Abu Bakr on the same day. The next day Fatima while she was accompanied by Ali (AS) went to Abu Bakr and said: "I want the inheritance left by the Prophet, my father."
Abu Bakr said: "Inheritance or gift?"
Fatima (SA) said: "As your daughters will inherit you, so am I entitled to inheritance of my father, Fadak, Khaybar and the properties which my father had in Medina and which he used to spend for charity."
Abu Bakr said: "By Allah, your father was better than me and you are also better than my daughters but the Prophet said that we the prophets do not leave any inheritance. Whatever is left by us will be spent on charity. Do you believe that your father gifted you these properties during his lifetime? By Allah, if you give me an answer in the positive, I will accept."
Fatima said: "Umm Ayman informed me that my father had gifted me these properties."
Abu Bakr said: "Did you hear your father say that? If you say 'yes', I will accept you.
Fatima said: "I said what was necessary to be said."[8]
 

[1] Tabari, Abu Ja'far Muhammad bin Jarir, Jami' al-Bayan fi Tafsir al-Qur'an, vol.28, p. 24, Dar al-Ma'refah, Beirut, 1412 A.H.
[2] For instance, Sahih Bukhari, Chap. Kitabat al-Ilm, Illness of the Prophet (S) and His Demise; for further studies in this regard, refer to questions 1527, 4266, 10163 and 11083.
[3] An-Nisa, verse 11; Al-Ahzab, verse 6; Al-Baqarah, verse 180.
[4] Maryam, verse 6; al-Naml, verse 16.
[5] Unlike Shias who, on the basis of the (Hadith) Tradition of Thaqalayn, believe in the Quran and Ahlulbayt (AS) as two inseparable weighty things.
[6] Ibn Tayfur, Ahmad bin Abi Taher, Balaghat al-Nisa, p. 29, Qom, first edition (without date).
[7] Muhammad bin Sa'ad, Al-Tabaqat al-Kubra, vol.2, p. 241, Dar al-Kotob al-Ilmiyah, Beirut, 1410 A.H.
[8] Ibid.