Jim procured another key, of course, after Sherlock left with his.

He uses it now, after he thinks enough time has passed since he saw Sherlock slip upstairs. It's harder to tell in Milliways, with time being what it is, but judging from the tableau that greets him, he got it about right.

He removes his suit jacket, hanging it up with great care in his closet. Then he drops onto his bed, slinging an arm cozily over Sherlock.