Sayyiduna Ali (may Allah be pleased with him) says: A young woman from Khath'am addressed the Messenger of Allah (peace and blessings be upon him) and said: My father is old; the Hajj that Allah has made obligatory upon His servants has become obligatory upon him as well, but he does not have the ability to perform it; will my performing it on his behalf suffice for him? He (peace and blessings be upon him) said: "Yes." Al-Darawardi narrates it from Uthman bin Umar, and in this narration the words are: "If I perform it on his behalf, will it suffice for him?"
Hadith Referenceالسنن الكبرى للبيهقي / كتاب الحج / 8631