a woman from Khath'am asked the Prophet on the morning of the Day of Sacrifice: "O Messenger of Allah! The command of Allah to His slaves to perform Hajj has come, while my father is an old man and cannot sit firmly in the saddle. Can I perform Hajj on his behalf?" He said: "Yes. "  

أَنَّ امْرَأَةً مِنْ خَثْعَمَ سَأَلَتِ النَّبِيَّ ﷺ غَدَاةَ جَمْعٍ فَقَالَتْ يَا رَسُولَ اللَّهِ فَرِيضَةُ اللَّهِ فِي الْحَجِّ عَلَى عِبَادِهِ أَدْرَكَتْ أَبِي شَيْخًا كَبِيرًا لاَ يَسْتَمْسِكُ عَلَى الرَّحْلِ أَفَأَحُجُّ عَنْهُ قَالَ نَعَمْ  

(Another chain) with a similar report narrated from Ibn 'Abbas. (sahih)  

عَنِ ابْنِ عَبَّاسٍ مِثْلَهُ