I see that the hotel where he was staying, offers a complimentary breakfast. Why would he make a point of going out of the hotel to get 2 coffees if not to establish a timeline for Stephany's murder.
Why would someone who walks ahead of Stephany, doesn't even hold the door to his room open for her - do her the favour of providing coffee for breakfast. It strikes me that his usual method of operation, after getting whatever it was he was after (sex, money etc) would be just to kick the person out. That is if they were lucky enough to escape unscathed.
After spending a few hours with him, it would have been apparent that he was no gentleman, and if he did leave the room, Stephany, if not drugged (or deceased) would have got out of there as soon as possible, not taken the time, to do a search on his (probably password protected) laptop. She could do her search after she had left there. In any case, I don't think he would not have left someone he had just met, in his room with all his belongings (money, passport, laptop etc).
I think Stephany was probably drugged shortly after she entered the room, and if by any chance the laptop shows that a search was made on him, then the sick ****** did it himself, and possibly showed her who he really was, when she was in no state to leave the room.
This guy should never ever get out of prison, as long as he lives. He is a cold blooded serial killer and that won't change.