Awful roommate left damages

So our roommate finally moved out but his stupid dog left stains and a hole in the carpet. We aren’t really sure how to tell management.... he wasn’t on the lease because our original roommate moved to another city so he just took his room.

We already told him he’s going to have to pay for it but we don’t know how to go about getting it replaced without getting into a lot of trouble. Should we just offer so that way it seems like we are trying to make amends? Or will it come out of the deposit? The rest of the apartment is in amazing condition. I like to keep it clean and I always report problems to maintenance first thing.

My boyfriend wants to tell them that a friend stayed over and he fucked it up but I just don’t know...