Muwatta Imam Malik (Riwayat Ibn al-Qasim)

It is narrated from Sayyiduna Ibn Abbas (may Allah be pleased with them both) that Fadl bin Abbas (may Allah be pleased with them both) was sitting behind the Messenger of Allah (peace and blessings of Allah be upon him) on a mount, when a woman from the tribe of Khath'am came to the Messenger of Allah (peace and blessings of Allah be upon him) to ask a question. Fadl bin Abbas (may Allah be pleased with them both) began to look at her and she began to look at Fadl bin Abbas. So the Messenger of Allah (peace and blessings of Allah be upon him) turned Fadl's face to the other side. The woman said: "O Messenger of Allah! Allah the Exalted has made Hajj obligatory upon His servants at a time when my father has become very old. Should I perform Hajj on his behalf?" The Messenger of Allah (peace and blessings of Allah be upon him) said: "Yes!" And this incident took place during the Farewell Pilgrimage.

It is narrated from Sayyiduna Abdullah bin Abbas (may Allah be pleased with them both) that a man came to the Messenger of Allah (peace and blessings be upon him) and said: O Messenger of Allah! My mother is very old, we cannot make her ride a camel, nor can she sit firmly. If I tie her to the mount, I fear she may die. Can I perform Hajj on her behalf? The Prophet (peace and blessings be upon him) said: "Yes!"