Has Lupin Taught before?

[Aurora Mendelsohn]

No: HPFGUIDX 29402

In PoA, on the train on the way to Hogwarts, Lupin's bag is describes as being frayed and worn out with a worn out name "*
Professor* R.J. Lupin" (IIRC). Isn't this his first time as a professor at Hogwarts? How can the name on his bag be worn out if the 
title professor is new to him? Did I miss something? Has he taught before ( at Hogwarts before Harry'stime or somewhwere else)?

Aurora