The CAA whose authority you fly under will have copies of each LPC you have carried out for the last five years.
You may politely direct your prospective employer to said authority. It's a process I'm in the middle of as we speak (type!!) as my prospective new employer wants these documents.
I must confess to having some of the same frustrations as Algol. Why would my new employer want all this additional paperwork if they like me and my sim check went OK?
I can only guess that in todays world of litigation, maybe insurance costs are reduced if the airline is able to "prove" to an insurer that their new guy has an impeccable history.
As I say, that's just a guess but I have no doubt that this measure is either bean counter or beaurocrat driven if demanded by the airline. If it's the local CAA who are demanding it, then maybe it's a bit of an "olive branch" that's been given to the local unions to justify employing an ex-pat.