Reference: Sharh Sunan Abu Dawood: 9/399
Al Fadl ibn ‘Abbaas – may Allaah be pleased with him – was seated behind the Prophet – صلى الله عليه وسلم – during the trip from Muzdalifah to Mina when a woman from Kath’am approached the Prophet inquiring about performing Hajj on behalf of her father, an old man who was unable to sit steadily on a riding animal, she asked: “The obligation of Hajj has come upon my father in his old age and he is unable to sit steadily on a riding animal, should I perform Hajj on his behalf?”
He responded: “Yes.”
This was during the farewell pilgrimage and attests that a woman can perform Hajj on behalf of a man, because the Messenger – صلى الله عليه وسلم – issued her a Fatwa to perform Hajj on behalf of her father.
This Hadeeth is also evidence that a person can perform Hajj on behalf of someone else; a man may perform Hajj on behalf of another man, and a woman may perform Hajj on behalf of a man, and this Hadeeth is clear evidence for women performing Hajj on behalf of men.