Certainly no problem accepting the money back, there isn't any rule in this regard. But I do think it was a little cheap. I would have turned it down at least the first offer. If insisted then sure, but you were paying by the month, so getting half back does seem cheap.
He offered, but did you hint at all? I think it's a grey area, so it's really hard for us to judge. If he knew money was tighter for you and wanted to help you out, then just accept as a gift and be thankful. But if he felt pressured then it might have been just a formality hoping/assuming you would say no, which you should have in my view. But none of that makes it right or wrong, nothing wrong with accepting it and nothing to regret greatly either way. I would send a nice personal note thanking him for refunding they money despite not needing to, and how much that is appreciated while moving, etc. Seems like a nice guy, good to let him know that.