The rules about ATCO licenses in the EU are all described on the EASA website at
https://www.easa.europa.eu/regulatio...ic-controllers. Somewhere in there you'll find the rules and procedures for transferring license issue from one Competent Authority/State to another (I can't recall the details because it's a while since I was involved in that stuff).
However, having a license with the relevant rating(s) is only one part of what makes a controller employable and attractive to a range of employers - experience is also important, that is to say, demonstrating that you can actually do the job. You might be well advised to get the licence (which in most situations is not a foregone conclusion simply because you are on a training course) and then get a couple of years experience behind you be looking for other employment opportunities. Who knows, your present employer might even offer further rating training and a move to a unit which is more to your liking.