Is it permissible for someone performing Hajj Mutamatti' to perform Hajj on behalf of one person and Umrah on behalf of another?

It is permissible for a person to perform Hajj as a Mutamatti' (combining 'Umrah and Hajj) intending the 'Umrah on behalf of one person and the Hajj on behalf of another, provided that he has already performed Hajj and 'Umrah for himself. He will be required to offer the sacrifice for Tamattu'. The intention of Tamattu' is not a condition for the obligation of the sacrifice, nor is it required that both rituals be performed on behalf of the same person. Rather, the sacrifice becomes obligatory even if the two rituals are performed on behalf of two different individuals, neither of whom is the pilgrim himself, or if one is for the pilgrim and the other for someone else.