Fokker, he is (or is entitled to be) a British citizen. No immigration restrictions can or will apply.
Surf0, the process of converting toa JAA licence is covered
here. I suggest you talk to a 737 TRTO over here to get quotes on either obtaining a TR from scratch or converting an NZ TR. It may well prove cheaper to do the lot here. As for expecting an airline to pay for the conversion for you, dream on! Despite the healthy market for pilots, there are no shortages appearing at the bottom of the market - where you would start. Your experience would put you ahead of the pack, but wouldn't buy you any special treatment.
Scroggs