When you say "his revenge", can "his" refer to the person on whose behalf said revenge is being taken?

In general usage it is her revenge, as you suspect. I also argue in the following way. She is the one seeking to harm another so as to gain satisfaction for the wrong done to her (loss of her friend, lover, or whatever he was). The revenge will therefore be hers. The victim is dead so he cannot harm anyone and therefore revenge cannot be his.