Question
When one is performing a Tamattu‘ Hajj, can he perform ‘Umrah on behalf of one person and Hajj on behalf of someone else?

Fatwa
All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.

There is nothing wrong if a person who performs a Tamatt' Hajj intends to perform ‘Umrah on behalf of one person and Hajj on behalf of another given that he has already performed Hajj and ‘Umrah for himself. However, he is required to offer a sacrificial animal pertaining to the Tamattu' Hajj. Shams Ad-Deen Ar-Ramli, a Shaafi‘i scholar said, “It is not a condition for the obligation of offering a sacrificial animal that the Hajj is intended as Tamattu‘ Hajj, that both the Hajj and ‘Umrah are done on behalf of the same person or that the person will remain alive until the Hajj is over.”

Ash-Shabraamallissi a Shaafi‘i scholar said, "…Nor (is it) that both the Hajj and ‘Umrah are to be performed on behalf of the same person". Meaning that offering a sacrificial animal is obligatory even if the Hajj and ‘Umrah are performed on behalf of two different persons other than the one who actually entered the state of Ihraam (ritual consecration) to perform them or if one of them (i.e. the Hajj or ‘Umrah) is performed on behalf of the person who is in the state of Ihraam, himself, and the other on behalf of someone else.

Allah Knows best.