It is narrated from Sayyiduna al-Fadl bin Abbas (may Allah be pleased with him) that he was riding behind the Prophet (peace and blessings be upon him) when a man came to him and said: "O Messenger of Allah! My mother is very old; if I mount her (on a riding animal), she cannot hold herself steady, and if I tie her, I fear that I may cause her death. Shall I perform Hajj on her behalf?" He (peace and blessings be upon him) said: "What do you think, if your mother owed a debt, would you pay it off on her behalf?" He said: Yes. He (peace and blessings be upon him) said: "Then perform Hajj on behalf of your mother."
Hadith Referenceالمعجم الكبير للطبراني / باب الفاء / 15849