Sahih Al Bukhari Hadith Number 1953

Narrated Ibn `Abbas: A man came to the Prophet (peace be upon him) and said, “O Allah’s Messenger (peace be upon him)! My mother died and she ought to have fasted one month (for her missed Ramadan). Shall I fast on her behalf?” The Prophet (peace be upon him) replied in the affirmative and said, “Allah’s debts have more right to be paid.” In another narration a woman is reported to have said, “My sister died…” Narrated Ibn `Abbas: A woman said to the Prophet (peace be upon him) “My mother died and she had vowed to fast but she didn’t fast.” In another narration Ibn `Abbas is reported to have said, “A woman said to the Prophet, “My mother died while she ought to have fasted for fifteen days.”

30  Fasting
Hadith number 1953
Volume no 3
Chapter: 42 (Can somebody else observe Saum instead of the dead?)