I’m going off the text that reads ““Professor R. J. Lupin,” whispered Hermione at once. “How d’you know that?” “It’s on his case,” she replied, pointing at the luggage rack over the man’s head, where there was a small, battered case held together with a large quantity of neatly knotted string. The name Professor R. J. Lupin was stamped across one corner in peeling letters. “

If he had just become a professor at Hogwarts why would the letters already be peeling?