It is narrated from Ibn Abbas (may Allah be pleased with them both) that a man came to the Prophet (ﷺ) and said: "O Messenger of Allah! My mother is very old, she does not have the strength to ride on a camel, and if I tie her on, I fear she may die. Should I perform Hajj on her behalf?" The Prophet (ﷺ) said: "Yes."
Hadith Referenceمسند الإمام الشافعي / كتاب الحج / 934