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."

حَدَّثَنَا مُوسَى بْنُ إِسْمَاعِيلَ، حَدَّثَنَا أَبُو عَوَانَةَ، عَنْ أَبِي بِشْرٍ، عَنْ سَعِيدِ بْنِ جُبَيْرٍ، عَنِ ابْنِ عَبَّاسٍ ـ رضى الله عنهما ـ أَنَّ امْرَأَةً، مِنْ جُهَيْنَةَ جَاءَتْ إِلَى النَّبِيِّ صلى الله عليه وسلم فَقَالَتْ إِنَّ أُمِّي نَذَرَتْ أَنْ تَحُجَّ، فَلَمْ تَحُجَّ حَتَّى مَاتَتْ أَفَأَحُجُّ عَنْهَا قَالَ ‏ "‏ نَعَمْ‏.‏ حُجِّي عَنْهَا، أَرَأَيْتِ لَوْ كَانَ عَلَى أُمِّكِ دَيْنٌ أَكُنْتِ قَاضِيَةً اقْضُوا اللَّهَ، فَاللَّهُ أَحَقُّ بِالْوَفَاءِ ‏"‏‏.‏



Reference : Sahih al-Bukhari 1852
In-book reference : Book 28, Hadith 32
USC-MSA web (English) reference : Vol. 3, Book 29, Hadith 77
(deprecated numbering scheme)