Originally Posted by gilbertaue

What you can also try - no guarantees:

The transit counters are typically around the area where the escalators go down to immigration (which you would need to go through if they really can't check through). What you can do is quickly check at the transit counter if they can retrieve your luggage for you and transfer to the GA flight and issue your BP. It can sometimes be done.
But only try this if there is no queue at the transit counters.

If that fails, just retrieve your luggage in Terminal1 where you arrive, head out and go up one floor to the departure level. Follow the signs to "Terminal 3" and take the aerotrain across. Doesn't take long.