Well, the answer to that is fairly simple my brothers and sisters. It is permissible for the Qurbani to be done on behalf of someone else, a relative of ours who has passed away and we can combine our intention of offering that sacrifice for the deceased family member with the animal that we are sacrificing for our own family. So, that’s a simple way of going about it. It was not a typical practice of the Prophet (peace be upon him) or of the Sahaba (may Allah be pleased with them) to actually sacrifice an animal specifically for someone else who had already passed away. But the Prophet (peace be upon him), he did himself offer the intention of the sacrificial animal to be offered to Allah (SWT), for the sake of Allah (SWT) on behalf of a family member of his that had passed away.
Now, the next question is can we offer an animal or sacrifice that animal for Allah (SWT) on behalf of the Prophet (peace be upon him), the answer to that is that the Prophet (peace be upon him) does not need that from us. Why? How? Very simply, Prophet Muhammad (peace be upon him) taught us our deen, he taught us our religion and everything that we need to know and do, and so the Prophet (peace be upon him) does not need us to sacrifice an animal on his behalf because when we sacrifice the animal and follow his Sunnah, by default, he is already being rewarded for that. And so no, it is not something that we are encouraged to do and recommended to do to offer an animal specifically for the Prophet (peace be upon him).