It was narrated from 'Abdullah bin 'Abbas that: a man asked the Prophet (ﷺ) "The command of ) Hajj has come while my father is an old man and cannot sit firmly in his saddle; if I tie him (to the saddle) I fear that he will die. Can I perform Hajj on his behalf?" He said: "don't you think that if your father owed a debt and you paid it off, that would be good enough?" He said: "Yes." He said: "Then perform Hajj on behalf of your father. "
Source: sunnah.com
Other translations
Arabic
أَخْبَرَنَا مُجَاهِدُ بْنُ مُوسَى، عَنْ هُشَيْمٍ، عَنْ يَحْيَى بْنِ أَبِي إِسْحَاقَ، عَنْ سُلَيْمَانَ بْنِ يَسَارٍ، عَنْ عَبْدِ اللَّهِ بْنِ عَبَّاسٍ، أَنَّ رَجُلاً، سَأَلَ النَّبِيَّ صلى الله عليه وسلم أَنَّ أَبِي أَدْرَكَهُ الْحَجُّ وَهُوَ شَيْخٌ كَبِيرٌ لاَ يَثْبُتُ عَلَى رَاحِلَتِهِ فَإِنْ شَدَدْتُهُ خَشِيتُ أَنْ يَمُوتَ أَفَأَحُجُّ عَنْهُ قَالَ " أَرَأَيْتَ لَوْ كَانَ عَلَيْهِ دَيْنٌ فَقَضَيْتَهُ أَكَانَ مُجْزِئًا " . قَالَ نَعَمْ . قَالَ " فَحُجَّ عَنْ أَبِيكَ " .
sunnah.com