Transfering work permit/ARC between government departments

Hi. i’m about to transfer my visa/ARC. both my present and future employers are happy to do this. No problem. But I will be transferring them between govt. departments ( I was previously a ‘language consultant’ and my work visa was given by the Economics ministry, and I will now be a ‘teacher’ - under the education ministry). I know this can be done due to a recent law change, but nobody concerned (me included) seems to know exactly how to go about it. I’ve had it transferred the other way around before- this is easy. I will have my bosses call the education department, but in the meanwhile- anybody have any experience/advice about this situation? Cheers.

The law change is new- until recently, Transfering visas/ARCs this way was apparently impossible.