Hi, we just transferred our entry stamp since we had new passports. If you're leaving, it's not required to have it transferred. If you're looking for a new visa, it is required to have it transferred.
We had to go back several times to get this accomplished.
Our first challenge was that our landlord never registered us, so we were not "in the system." You need to be registered to an address in the same province of the immigration office you're visiting. It's good to show up with a copy of your landlord's ID card, hotel/homestay permit, and their address & phone #.
Then you need a photocopy of every single page of your passport (like 30 pages), a photocopy of the front and back of the Departure Card, and photocopy of the first page of your new passport.
Once you have all of that, it takes around 10 minutes.