No, he's not living there...he's been in her apartment in a few episodes, but she hasn't moved in with Leonard yet-oh, and FYI in the future put a question like this in the "Answers" section of the club. :D

Hi has this happened since the robbery ? and thank you for the FYI I'll know next time I'm new here

Um...he was in her apartment a little in episode 3.16...the robbery was 3.13 I believe. So he has been there since the robbery-but no one is moving.

Yeah, that's fine-no one's gonna kick you out or anything!

But! all of his things are in the small apartment like the dartboard on the back of the door and her blue/greenish sofa is in the big apartment so here's the thing your sure no one's moved? we are only up to episode 11 over here

Ok, her blue sofa is still in her apartment, some of Leonard's things are in Penny's apartment, and some of her things are in his, but Sheldon is the same. You're either confusing Sheldon and Leonard or you're confusing the apartments, I don't know. We're up to episode 16 here, 17 on Monday, and I've read spoilers through episode 19, and no one's going anywhere as of now.

No I'm just not seeing this sorry to drag it out but in the episode with Stan Lee when Wolowitz get's a paper cut Sheldon tell's him where to find a sticking plaster and Wolowitz find's all the pay cheques that's all in the small apartment ie' Penny's old apartment
"what can I say wine and late nights"

No, that was in Leonard and Sheldon's apartment.