Have you tried vegan cheese ?

what an unfortunate allergy! is it the lactose?

I don’t know what the allergy but Lactose is a common one. is but you can buy Lactose free cheese, milk, yoghurt. cream, icecream. Butter is also made from milk. . Lactose is the natural sugar in cow’s milk. Cheese is “concentrated” so he may be more allergic to it than jsut milk. Milk also has casein in it. (I don’t actually know what that is).
This may or may not help you. I have 2 close friends (sisters) who are lactose intolerant. One of them can’t even have plain or savoury biscuits with milk in them.
Is your partner able to find out what the actual allergy to cheese is, whether it is something that is used in the manufacture of it??? Is it possible It may also depend what type of cheese you are using (e,g, cheddar, matured, parmesan etc.) Would he be able to taste/eat just a tiny bit of lactose free cheese to see if he has any reaction???
Is he also gluten intolerant??? Some ready grated cheeses have flour mixed in them to stop it from sticking together.
I wish you well in finding a solution. It must be very frustrating for your partner too. Do his parents know any details that may help get some resolution or isn’t an option to ask them?