From my limited understanding in my jurisdiction (in the US) he probably does indeed own the copyright to the code in question.

I have no knowledge of what sort of implied licenses may have been generated, but I would feel comfortable (aside from technical risk) continuing to run those JARs in production for the short term.

As a bit of unsolicited advice, have you asked him how much he is willing to sell a license to the code for? Depending on the price, it may be a good win/win solution for you.