Sahih Muslim Book 6, Hadith Number 2554.

Chapter : Completing of the fast on behalf of the dead.

Ibn ‘Abbas (Allah be pleased with both of them) reported: A woman came to the Messenger of Allah (may peace be upon him) 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).