As soon as Remus reads the owl, the only hesitation that keeps him from moving towards the door at once is that he wonders if Sirius will be upset for him talking to Harry first. But maybe if he speaks with Harry he will be able to calm him down in case he's still upset at Sirius...

Going with that thought, Remus leaves a note for Sirius on the table saying he will be back soon before leaving his quarters to cross the hall.

With a couple of knocks on the door, and a small pause, he opens the door and lets himself in the apartment. Upon seeing him on the couch, Remus' lips tug very slightly but he doesn't move closer just yet. "Good morning."