It is narrated from Sayyiduna Ibn Abbas (may Allah be pleased with them both) that in the year of the Farewell Hajj, a woman came to the Messenger of Allah (peace and blessings be upon him) and said: O Messenger of Allah! My father is a very old man; he cannot hold steady on a mount. Will 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 / 15815