Sahih Muslim Book 7, Hadith Number 3090.

Chapter : One may perform Hajj on behalf of the maimed, the old and the deceased.

Fadl reported that a woman of Banu Khath’am said: Messenger of Allah, my father is very old. There is an old obligation of Hajj upon him from Allah, but he is not capable of sitting on the back of the camel. Thereupon Allah’s Apostle (may peace be upon him) said: Perform Hajj on his behalf.