All perfect praise be to Allaah, The Lord of the worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu ‘alayhi wa sallam, is His slave and Messenger.
There is nothing wrong if a person who performs a Tamattu‘ Hajj intends to perform ‘Umrah on behalf of one person and Hajj on behalf of another given that he had 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 conditioned 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 remains alive until the Hajj is over."
Ash-Shabraamallisi, a Shaafi‘i scholar said: "…nor that both the Hajj and ‘Umrah are performed on behalf of the same person." Meaning that offering a sacrificial animal is obligatory even if both the Hajj and ‘Umrah are performed on behalf of two different persons other than the one who actually entered the state of Ihraam to perform them or if one of them (i.e. Hajj and ‘Umrah) is performed on behalf of the person who is in the state of Ihraam, himself, and the other on behalf of someone else."
Allaah Knows best.