It is narrated from Sayyiduna Ibn Abbas (may Allah be pleased with them both) that a woman from the tribe of Khath'am asked the Messenger of Allah (peace and blessings be upon him) for a ruling: "The obligation of Allah upon His servants regarding Hajj has reached my father while he is a very old man; he cannot sit upright on a mount. Would my performing Hajj on his behalf suffice for him?" The Messenger of Allah (peace and blessings be upon him) said: "Yes."
Hadith Referenceالمعجم الكبير للطبراني / باب الفاء / 15819