Waitinggent

Much thanks to all who spent the time to post their wisdom. It was quite helpful, and the situation seems to be resolved. There is a website called CBP.GOV which has a contact phone number. By calling this number, I was able to get a phone number for the CBP at our airport and get the location. They said that all was in order except that they failed to take the envelope. I thought that was probably the case since the I-94 was stamped and the officer had written K2 inside the stamp.

I am far from expert in this, but my understanding is that he has to be in the USA at least 1 time every six months. Personally, I don't have a problem with what you are doing, but as others have posted, the green card will likely be revoked eventually when it becomes obvious that he is not really living here.
And unlike 1 poster, I am certainly not surprised that he prefers to continue to live in his native country rather than emigrate to the USA. I am sure that most Europeans would prefer to live where they are rather than emigrate to the USA and start life over at the bottom.