@John ******
you don’t need to get a copy of the TM30, done by the hotel. Their entry will be on the system. You should go to your local Immigration Office, within 24 hours of your arrival at your GF’s home to register a TM30 with them.
When I went through the same procedure, a couple of months ago, 2 paper receipts were stapled into my passport, one of which said that I should report again, in 90 days. It actually stated which date that was.