To perform Hajj on behalf of a dead person. A man can perform Hajj on behalf of a woman
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 ".
Narrated Ibn `Abbas: A woman from the tribe of Juhaina came to the Prophet (ﷺ) 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 (ﷺ) 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."