Is everything reported by al-Tabari regarding the death of Fatimah al-Zahra and her will to her husband Ali ibn Abi Talib correct?

Fatimah (may Allah be pleased with her) lived for six months after the Prophet (peace and blessings be upon him) and then passed away. She was buried at night. Ali (may Allah be pleased with him) buried her at night according to her will, for the sake of greater concealment. It is not established that Abu Bakr was not informed of her death by her order. Rather, it is reported that Abu Bakr prayed over her, and there is nothing in the narration to indicate that he was unaware or did not attend her funeral.