I am not sure I understand what you mean exactly. You can't just "switch" fire departments without the "process", at least I am not aware of any. If I wanted to move, I would have to do most, if not all of the "process" over again... complete with no guarantees.
Really? You move from city A to city B and have to go back to fire fighter school?
Admittedly I don't know very many firefighters but the way in for some was to get in a small city, then move to a larger one as they were already in the club so to speak. I don't believe they started at the bottom rung again.