First: I would never ever even share a home with someone who doesn't like (my) pets, let alone really moving in together.

My first suggestion: dump the boyfriend, but that seems to be out of the question.

Maybe she can ask the boyfriend to have a very big cage for the dog too? If he thinks that's a stupid idea, he might get the picture.

If he doesn't like her cats, the cats won't like him either. Maybe she should really think about rehoming them somewhere nice and she can visit the cats sometimes? But making such a bit sacrifice already at the beginning... well, I don't think this works out.