I’ve made the move from overseas back to the US and in my case, my current airline simply had to “ask” for my training records to meet the requirements of the PRIA. They don’t actually have to be provided with those records from a foreign employer and in many cases, foreign employment laws forbid it, anyway.
As an airline won’t apply for your records until after they’ve offered you a job, they’ll know from an interview, whether or not you have the experience you’ve claimed, simply by asking the right questions.