كتاب الحج
15  
The Book of Pilgrimage
(71)
Chapter: Hajj on behalf of one who is incapable of doing it because of chronic illness, old age and the like, or on behalf of one who has died
(71)
باب الْحَجِّ عَنِ الْعَاجِزِ، لِزَمَانَةٍ وَهِرَمٍ وَنَحْوِهِمَا أَوْ لِلْمَوْتِ ‏‏
Sahih Muslim 1334

'Abdullah b. 'Abbas reported that while al-Fadl b. Abbas had been riding behind Allah's Messenger (ﷺ) a women of the tribe of Khath'am came to him (to the Holy Proppet) asking for a religious verdict. Fadl looked at her and she looked at him. Allah's Messenger (ﷺ) turned the face of al-Fadl to the other side. She said:

Messenger of Allah, there is an obligation from Allah upon His servants in regard to Hajj. (But) my father is an aged man; he is incapable of riding safely. May I perform Hajj on his behalf? He said: Yes. It was during the Farewell Pilgrimage.
حَدَّثَنَا يَحْيَى بْنُ يَحْيَى، قَالَ قَرَأْتُ عَلَى مَالِكٍ عَنِ ابْنِ شِهَابٍ، عَنْ سُلَيْمَانَ بْنِ، يَسَارٍ عَنْ عَبْدِ اللَّهِ بْنِ عَبَّاسٍ، أَنَّهُ قَالَ كَانَ الْفَضْلُ بْنُ عَبَّاسٍ رَدِيفَ رَسُولِ اللَّهِ صلى الله عليه وسلم فَجَاءَتْهُ امْرَأَةٌ مِنْ خَثْعَمَ تَسْتَفْتِيهِ فَجَعَلَ الْفَضْلُ يَنْظُرُ إِلَيْهَا وَتَنْظُرُ إِلَيْهِ فَجَعَلَ رَسُولُ اللَّهِ صلى الله عليه وسلم يَصْرِفُ وَجْهَ الْفَضْلِ إِلَى الشِّقِّ الآخَرِ ‏.‏ قَالَتْ يَا رَسُولَ اللَّهِ إِنَّ فَرِيضَةَ اللَّهِ عَلَى عِبَادِهِ فِي الْحَجِّ أَدْرَكَتْ أَبِي شَيْخًا كَبِيرًا لاَ يَسْتَطِيعُ أَنْ يَثْبُتَ عَلَى الرَّاحِلَةِ أَفَأَحُجُّ عَنْهُ قَالَ ‏ "‏ نَعَمْ ‏"‏ ‏.‏ وَذَلِكَ فِي حَجَّةِ الْوَدَاعِ ‏.‏
Reference : Sahih Muslim 1334
In-book reference : Book 15, Hadith 455
USC-MSA web (English) reference : Book 7, Hadith 3089
  (deprecated numbering scheme)
Sahih Muslim 1335

Fadl reported that a woman of Banu Khath'am said:

Messenger of Allah, my father is very old. There is an old obligation of Hajj upon him from Allah, but he is not capable of sitting on the back of the camel. Thereupon Allah's Apostle (ﷺ) said: Perform Hajj on his behalf.
حَدَّثَنِي عَلِيُّ بْنُ خَشْرَمٍ، أَخْبَرَنَا عِيسَى، عَنِ ابْنِ جُرَيْجٍ، عَنِ ابْنِ شِهَابٍ، حَدَّثَنَا سُلَيْمَانُ بْنُ يَسَارٍ، عَنِ ابْنِ عَبَّاسٍ، عَنِ الْفَضْلِ، أَنَّ امْرَأَةً، مِنْ خَثْعَمَ قَالَتْ يَا رَسُولَ اللَّهِ إِنَّ أَبِي شَيْخٌ كَبِيرٌ عَلَيْهِ فَرِيضَةُ اللَّهِ فِي الْحَجِّ وَهُوَ لاَ يَسْتَطِيعُ أَنْ يَسْتَوِيَ عَلَى ظَهْرِ بَعِيرِهِ ‏.‏ فَقَالَ النَّبِيُّ صلى الله عليه وسلم ‏ "‏ فَحُجِّي عَنْهُ ‏"‏ ‏.‏
Reference : Sahih Muslim 1335
In-book reference : Book 15, Hadith 456
USC-MSA web (English) reference : Book 7, Hadith 3090
  (deprecated numbering scheme)