Reference: Sunan Abu Dawood: 9/400
One cannot perform Hajj on behalf of a living person except in two cases:
The First: The situation that was narrated in this Hadeeth, and it is that the person whom Hajj is being performed on behalf is an old person who cannot sit steadily on a riding animal.
The second: That the person has an illness that he/she does not expect to be cured of.
Other than these two categories of people, one cannot perform Hajj on behalf of the living.