All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.
Faatimah the daughter of the Prophet, sallallaahu ‘alayhi wa sallam, could not have died while supplicating against the best man in this Ummah (Muslim nation) after her father. We do not know the origin of this supplication.
However, what is proven is that after the death of the Prophet, sallallaahu ‘alayhi wa sallam, Faatimah asked Abu Bakr to give her share of her father’s inheritance. Abu Bakr told her that he heard the Prophet, sallallaahu ‘alayhi wa sallam, saying that the property of the prophets is not to be inherited, and whatever they leave is to be given out as charity. Therefore, she never spoke to him again until she died. [Al-Bukhari and Muslim].
Al-Haafith Ibn Hajar commented on this Hadeeth in good terms. He reported Ma‘mar and At-Tirmithi saying that this Hadeeth means that Faatimah never spoke again with Abu Bakr about the matter of her inheritance until she died. However some object to this interpretation, saying that the wording of the Hadeeth imply that Faatimah deserted Abu Bakr . Then Ibn Hajar reported that some senior scholars believe that this desertion, if true, means that she preferred not to meet with him, but this is not considered prohibited desertion. In fact, prohibited desertion is when two parties see each other but refuse to talk. So it seems that after Faatimah had left Abu Bakr feeling angry, she was preoccupied with her grief then with her sickness.
As for the reason for her anger, despite the Hadeeth that Abu Bakr mentioned to her, it is because she believed that the meaning of this Hadeeth differs from the meaning that Abu Bakr adhered to. However when Abu Bakr insisted on his opinion, she stopped meeting with him. It seems that she believed that the profits of lands and real estate which the Prophet, sallallaahu ‘alayhi wa sallam, left could be inherited, while Abu Bakr insisted on applying the general meaning of the mentioned Hadeeth.
There is a Hadeeth narrated by Ash-Sha‘bi where it is mentioned that Abu Bakr visited Faatimah and she allowed him to enter the house after asking the permission of ‘Ali, may Allaah be pleased with all of them. Abu Bakr kept on conciliating her until she was conciliated. [This was narrated by Al-Bayhaqi without mentioning the narrator next to the Taabi‘i. However its chain of narrators up to Ash-Sha‘bi is authentic: Al-Haafith ibn Hajar].
If this Hadeeth is true, then there is no confusion. Most probably it is true because Faatimah was known for her wisdom and piety.
Allaah Knows best.