Just for info, I have a friend (also from Gothenburg) who just finished his conversion. He did his written tests in sweden and then the swedish CAA sent an examiner over to Dallas where he did the checkride in the Learjet sim.
He did a FAA recurrent on the Lear and then added a extra day to do the JAA checkride with the swedish examiner in the back. Not a bad way to get the conversion done. And you end up with a JAA Learjet type also. So that's a bonus. Just something to think about.