Hang on.... if you have an IMCR renewal, does anything get sent to the CAA??
I went to a CAA presentation on the IMCR a couple of years ago, and they said they thought about 20,000 IMC Ratings have been issued since 1969 or so, but they could not be sure because after the initial IMCR checkride they don't get any paperwork when people renew it.
The renewal is just a logbook signoff by a suitably authorised instructor. I reckon you could do it in Mongolia.