It was narrated from 'Abdullah bin 'Abbas that:

A man asked the Messenger of Allah ﷺ: "The (command to perform) Hajj has come while my father is an old man and cannot sit firmly in the saddle, and if I tie him, I fear that he may die. Can I perform Hajj on his behalf?" He said: "Do you think that if he owed a debt you would pay it off for him?" He said: "Yes." He said: "Then perform Hajj on behalf of your father."

أَخْبَرَنَا مُجَاهِدُ بْنُ مُوسَى، عَنْ هُشَيْمٍ، عَنْ يَحْيَى بْنِ أَبِي إِسْحَاقَ، عَنْ سُلَيْمَانَ بْنِ يَسَارٍ، عَنْ عَبْدِ اللَّهِ بْنِ عَبَّاسٍ، أَنَّ رَجُلاً، سَأَلَ النَّبِيَّ ﷺ إِنَّ أَبِي أَدْرَكَهُ الْحَجُّ وَهُوَ شَيْخٌ كَبِيرٌ لاَ يَثْبُتُ عَلَى رَاحِلَتِهِ فَإِنْ شَدَدْتُهُ خَشِيتُ أَنْ يَمُوتَ أَفَأَحُجُّ عَنْهُ قَالَ " أَفَرَأَيْتَ لَوْ كَانَ عَلَيْهِ دَيْنٌ فَقَضَيْتَهُ أَكَانَ مُجْزِئًا ". قَالَ نَعَمْ. قَالَ " فَحُجَّ عَنْ أَبِيكَ ".