The procedure for arriving and then continuing on a connecting flight from Terminal 2?

You mean you will have 1h20mins for the connection? I'm afraid time may not be enough even if you are in the same terminal. In some international airports, like Shanghai Pudong, check-in will be closed 45 minutes prior to the departure time. Besides, you also need some time to fetch your luggage for the first flight, then change the boarding pass for the connected one, check in your luggage again, pass the security, etc. In this case, i think 3 hours will be more safe.