The narrations claiming that the Prophet Muhammad (SAWA) instructed Abu Bakr to lead the prayers during his last sickness is not authentic at all. The main narrator is just one person who is Ayisha the daughter of Abu Bakr. Another narrator is 'O'rwah Ibn al-Zubair ,the sin of Asmaa' who is Ayisha's real sister. 'O'rwah was not even born in the time of incident, beside his own benefit to support his the claim of his aunt for political reasons. 'O'rwah fought against Imam Ali in the battle of Jamal (The Camel). He was a staunch enemy of Imam Ali (AS) till the end of his life.
Lot of people were present near the Prophet during his last sickness, but none of them narrated such incident. The Masjid was full of Muslims, but none of them narrated that the Prophet sent Abu Bakr to lead the prayers. On the contrary, authentic narrations stated that Ayisha while the Prophet was not well, told her father to go to the Masjid to lead the prayers with out informing the Prophet. When the Prophet was cane to know, he tolerated his heavy illness and went to the Masjid and dragged Abu Bakr back and led the prayers. If Abu Bakr was really sent by the Prophet to lead the prayer, then why did the Prophet drag him back and prevent him from leading the prayers.
Even if Abu Bakr was told to lead the prayers, which never happened, leading the prayers can never be an evidence to be a successor of the Prophet as it is a clear fact that the Prophet used to order a man (Ibn Abi Maktoom) to lead the prayers in his Masjid when he away from Madinah. Can any one claim that that man is the successor after the Prophet?
This fabricated story aims to justify ignoring the clear orders and obvious allegiance which was taken from Muslims in the Day of Ghadeer to follow Ali (AS) after the Prophet (SAWA).