Is it permissible to perform Hajj on behalf of someone without their knowledge, whether the one on whose behalf Hajj is performed is a man on behalf of an unrelated woman or vice versa?

Performing Hajj on behalf of a living person is not permissible unless they are incapacitated in a way that is not expected to be overcome. In the case of such incapacity, it is permissible for a woman who is not a mahram (a foreign woman) or anyone else to perform Hajj on behalf of a man, or vice versa. This is the view of the majority of scholars. For Hajj or Umrah performed on behalf of another to be valid, the permission of the living person must be obtained.