This hadith has been narrated on the authority of Ibn 'Abbas (Allah be pleased with them) from the Messenger of Allah (ﷺ).
Sahih Muslim Book 13, Hadith 201
← Previous Hadith 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.

Sahih Muslim Book 13, Hadith 200 Next Hadith → 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.

Sahih Muslim Book 13, Hadith 202