There is a dispute between him and his wife – should he pay zakaat al-fitr on her behalf?

Praise be to Allah.

A man is obliged to pay zakaat al-fitr on behalf of himself and of everyone on whom he is obliged to spend, which includes his wife, because he is obliged to spend on her. If there is a serious dispute between them, this may be regarded as nushooz (willful defiance) which means that he is no longer obliged to spend on her. In that case he does not have to pay zakaat al-fitr on her behalf, because it is connected to the obligation to spend on her, and if he is no longer obliged to spend on her then he is no longer obliged to pay zakaat al-fitr on her behalf. 

And Allaah is the Source of strength.