Narrated Ibn ‘Abbas:
A woman from the tribe of Juhaina came to the Prophet and said, “My mother had vowed to perform Hajj but she died before performing it. May I perform Hajj on my mother’s behalf?” The Prophet replied, “Perform Hajj on her behalf. Had there been a debt on your mother, would you have paid it or not? So, pay Allah’s debt as He has more right to be paid.”
Sahih Bukhari, Volume 3, Book 29, Number 77