J1 to green card
 

I'm American, and my new British husband and I are starting to work on his green card process. He is currently on a J-1 visa as a researcher, and he claimed the US/UK tax treaty for 1/2 year. Is the treaty automatically void (ie he'll owe back taxes) if he remains in the US longer than two years, even he changes his visa status to something other than a J-1 before then? What if he leaves the US before the 2 years of his J-1 are over and then reenters on another visa - will he owe back taxes then?
Thanks for any information!