aircraft can be flown in NZ but maintanence standards must comply with FAA and be signed off by FAA qualified LAME. If you convert to NZ register then the aircraft must be maintained to NZ standards. Don't know about the IF rating tho - if you were going to fly a NZ registered aircraft I think most certainly you would have to do some conversion.
Go to the NZCAA website and check the quicklinks to the regs and have a wee surf around to find the answer.