Leaseholding couple break up, one moves out. Is there a process?

[Johann Jells]

Sadly, a leaseholding couple has broken up and one is moving out. Never happened to us before. They're already on month to month, as we usually do after a 1 year lease. NJ has some strong anti-eviction law so what I could do is limited anyway if I had a problem with the remaining tenant, which I don't. His gross income alone (from 2 year old application) is 3x the rent.

My inclination is do nothing at all. Or do I really need to issue a new lease so he alone is legally liable?