If anyone dies in a state (that he had to complete) some fasts, his heir must fast on his behalf.
Sahih Muslim Book 13, Hadith 198
← Previous Hadith If one amongst us had to break fasts (of Ramadan due to natural reasons, i. e. menses) during the life of the Messenger of Allah (ﷺ) she could not find it possible to complete them so long she had been in the presence of Allah's Messenger (ﷺ) till Sha'ban commenced.

Sahih Muslim Book 13, Hadith 197 Next Hadith → 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).

Sahih Muslim Book 13, Hadith 199