'A'isha (Allah be pleased with her) reported Allah's Messenger (ﷺ) as saying
If anyone dies in a state (that he had to complete) some fasts, his heir must fast on his behalf.
Ibn 'Abbas (Allah be pleased with both of them) reported
A woman came to the Messenger of Allah (ﷺ) and said: My mother has died, and fasts of a month are due from her. Thereupon he said: Don't you see that if debt was due from her, would you not pay it? She said: Yes (I would pay on her behalf). Thereupon he said: The debt of Allah deserves its payment more than (the payment of anyone else).
Ibn 'Abbas (Allah be pleased with them) reported
A man came to the Messenger of Allah (ﷺ) and said: Messenger of Allah, my mother has died (in a state) that she had to observe fasts of a month (of Ramadan). Should I complete (them) on her behalf? thereupon he (the Holy Prophet) said: Would you not pay the debt if your mother had died (without paying it)? He said: Yes. He (the Holy Prophet) said: The debt of Allah deserves more that it should he paid.
This hadith has been narrated on the authority of Ibn 'Abbas (Allah be pleased with them) from the Messenger of Allah (ﷺ).
Ibn Abbas (Allah be pleased with them) reported
A woman came to the Messenger of Allah (ﷺ) and said: Messenger of Allah, my mother has died and there is due from her a fast of vow; should I fast on her behalf? Thereupon he said: You see that if your mother had died in debt, would it not have been paid on her behalf? She said: Yes. He (the Holy Prophet) said: Then observe fast on behalf of your mother.
Abdullah b. Buraida (Allah be pleased with him) reported on the authority of his father
When we were sitting with the Messenger of Allah (ﷺ), a woman came to him and said: I had gifted to my mother a maid-servant, and now she (the mother) has died. Thereupon he (the Holy Prophet) said: There is a definite reward for you and she (the maid-servant) has been returned to you as an inheritance. She (that woman) again said: Fasts of a month (of Ramadan) are due upon her; should I observe them on her behalf? He (the Holy Prophet) said: Observe fasts on her behalf. She (again) said: She did not perform Hajj, should I perform it on her behalf? He (the Holy Prophet) said: Perform Hajj on her behalf.
'Abdullah b. Buraida (Allah be pleased with him) reported on the authority of his father
I was sitting with the Messenger of Allah (ﷺ) ; the rest of the hadith is the same but with this variation that the (the narrator) said:" Fasts of two months."
Ibn Buraida (Allah be pleased with him) reported on the authority of his father
A woman came to the Messenger of Allah (ﷺ) , and the rest of the hadith is the same , but he said : " Fasting of one month." This hadith has been narrated on the authority of Sufyan with the same chain of transmitters in which it is said : " Fasting of two months." Buraida (Allah be pleased with him) reported a similar hadith on the authority of his father that a woman came to the Messenger of Allah (ﷺ) and he said : " Fasting for one month."