'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 (RA) reported: A man came to the Apostle 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.
Ibn Abbas (RA) 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 bin Buraida (RA) 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 bin Buraida (RA) reported on the authority of his father: I was sitting with the Apostle 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 (RA) reported on the authority of his father: A woman came to the Apostle of Allah (ﷺ) , and the rest of the hadith is the same, but he said: "Fasting of one month."
Buraida (RA) reported a similar hadith on the authority of his father that a woman came to the Apostle of Allah (ﷺ) and he said: "Fasting for one month."