Most companies I know are pretty strict about making sure they get licenses for any third-party code that goes into their system, including that written by employees. (I remember once, while working at Google, getting a request from a fellow Googler to "please add a LICENSE file to the PyJSDoc GitHub repository", because they wanted to use it for a project but couldn't without an explicit license, even though I was now working for the same company.) I've seen a few that also include blanket releases into their IP assignment docs, with wording along the lines of "You represent that you have the legal right to use any code that you incorporate into your employer's systems, and grant employer a perpetual royalty-free blahblahblah license to use any such code you authored that has been so incorporated."
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.