Who was the female Companion whom the Prophet (peace and blessings be upon him) shrouded with his own garment?

Al-Hafiz Ibn Hajar mentioned in "Al-Isabah" that the mother of Ali ibn Abi Talib, Fatimah bint Asad, is the one referred to in the hadith. He attributed a hadith to Ibn Abi Asim, narrated by Ali ibn Abi Talib, that the Prophet (peace be upon him) shrouded Fatimah bint Asad in his shirt and said, "We have not met anyone kinder to us after Abu Talib than her." Al-Hakim narrated the story of her shrouding in the Prophet’s garment, but Al-Dhahabi omitted it from "Al-Talkhis" due to its weakness.