Sayyiduna Abdullah bin Abbas (may Allah be pleased with them both) says: A woman from the tribe of Khath'am came to the Messenger of Allah (peace and blessings be upon him) in the year of the Farewell Pilgrimage to ask for a ruling. She said: O Prophet of Allah (peace and blessings be upon him), the obligation of Hajj that Allah has placed upon His servants has reached my father in old age, such that he cannot sit on a mount; will my performing Hajj on his behalf suffice for him? He (peace and blessings be upon him) said: "Yes."
Hadith Referenceالسنن الكبرى للبيهقي / كتاب الحج / 8626