After the short introduction, enter the room on your left. Meet up with Peppita
in room 509 located at the bottom right (Private Action.)

* When you exit, go up to the right at the little alcove there is a scene with
Peppita. If you cannot see it right away, try entering the transporter room to
the left of the stairs, then coming back out. It should activate. (Private
Action)

Fayt's room is room 506, just a few doors left. Watch the scene when you enter.
There is a save point you can use at the top of the room. Now get some rest in
your bed (the ones right below Sophia.)

The transporter that brought you to this facility is now configured to take you
to the Transport Ship Herle.