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. 
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