Can you be working remotely on your PhD thesis of another country and then enroll and get a master/PhD in US at the same time?
To my knowledge, there aren't any laws prohibiting anyone from joining a graduate program for any reason. It might be a problem if there is a conflict in grant funding or with the confidentiality needs of a particular research program, but otherwise it should be fine. He should Just make sure he fulfill any obligations in the programs. 

It would probably be best, just to avoid later questions, for your friend to be open with the new program about his relationship with the old one. But I don't think that is actually required. 

I wonder, of course, why the OP thinks two degrees are necessary and whether there is time to be faithful to both, but that isn't a legal concern.