Can we offer Qurbani on behalf of a dead person?

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When you sacrifice your Qurbani, you may intend to do it on your behalf and all your family members including the deceased ones by name or even by saying all deceased members of your family as a general statement.
This opinion is based on the following hadith:

On the authority of ‘Aishah (RAA), “Allah’s Messenger (PBUH) ordered a horned ram with black legs, a black belly and black around its eyes, and it was brought for him to sacrifice and he said to ‘Aishah (RAA), “Aishah, get the knife.” Then he said, “Sharpen it with a stone.” When she had done so he took it, then taking it (the ram) he placed it on the ground and slaughtered it. He then said, “Bismillah (In the name of Allah), O Allah, accept it from Muhammad, Muhammad’s family and from Muhammad’s Ummah (followers).” (Then he sacrificed it.’).

From this report, the scholars who approved this act extracted permisibility to slaughter on behalf of a dead person because it is well known that some of Muhammad`s Ummah are dead, and since our beloved Prophet presented the reward of slaughtering that ram for his Ummah, then offering a sacrifice on behalf of a deceased is permissible.