I don't think you are actually "converting" the FAA IR to a IMCR.
What happens is that you send the evidence of your FAA IR, plus the recent IPC signoff, and a cheque for about £60, to the CAA, and they stick an IMCR onto your UK PPL, but that IMCR is valid only as long as your FAA IR is valid and within the IPC deadline of 2 years.
Or do you actually get a standalone IMCR this way, which you can renew with an IMCR checkride, and allow the FAA IR to lapse?