Has my roommate breached a contract?

My husband and I rented out a room in our apartment to someone. He agreed to stay until August, but left after a week and did not tell us until he had already moved his stuff out. He had not signed onto the lease with the apartment complex, but we had made an agreement with him via text and Facebook Messenger. We told him that if he moved out, he had to pat his portion of the bills, as we had all agreed, until someone else took over the room. As of yet, no one has rented to room. If he refuses to pay, can we take him to court for breach of contract? And would we stand a chance of winning the case?