Who was the female companion whom the Prophet, sallallaahu alayhi wa sallam, enshrouded with his long shirt?

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.

Ibn Hajar mentioned that this female Companion was Faatimah bint Asad, the mother of 'Ali ibn Abi Taalib both. He mentioned a narration which he attributed to be reported by Ibn Abu 'Aasim that 'Ali narrated that the Prophet, sallallaahu ‘alayhi wa sallam, enshrouded Faatimah bint Asad in his long shirt and said: "We did not find after Abu Taalib a person who was more kind to us than her."

The story of the Prophet, sallallaahu ‘alayhi wa sallam, having enshrouded her in his long shirt is reported by Al-Haakim but Ath-Thahabi did not report it because it is a weak narration.

Allaah Knows best.