Back down in the hatch-hole, Desmond is still asking Locke, "Are you him?" Locke either decides it's in his best interest to say he is, or he just remembers the words of a wise Ghostbuster: "Ray, next time someone asks if you a god? You say yes!" Good advice. I have it in cross-stitch hanging by my desk. Locke stands up. "Yes I am," he says, smiling. "Can't believe it. You're finally here," says Desmond. "Well, here I am," says Locke, grinning. Don't oversell it, dude. Desmond looks at Kate, still lying on the floor. "Who's she?" Locke helps Kate to her feet, and finally just says, "She's with me." Given that Locke doesn't even know whom he's pretending to be, it's understandable that that was the best cover story he could come up with for Kate (much better than trying, "She's for you," and thrusting her at Desmond, I suppose).
Desmond seems quite perplexed by this, so he tests Locke: "What did one snowman say to the other snowman?" Locke does his best to come up with an answer (which is either "do you smell carrots?" or "drop your pants, here comes the snowblower," or "freeze!" depending on who you ask). Locke says, as nonchalantly as he can, that he has no idea what Desmond's on about. Desmond raises the rifle again, tightening his grip, and orders Locke to throw down the knife. "You're not him," he says.
Locke takes off his Rambo-sized knife and throws it to the side. "We didn't come here to hurt you," says Locke. Good thing, Locke, since Desmond's got the drop on you. Desmond wants to know why they did come here then, and Kate helpfully says that they were in a plane crash. Since that really doesn't answer Desmond's question, he says "Were you now," and asks when that was, and Locke says, "Forty-four days ago," and Desmond repeats this and thinks about it for a moment. Notice also that Desmond has a Dharma logo on his jacket.
Then he circles around them, still training the rifle on them, and he orders them to move. They pass by a wall covered with counting notches, four vertical strokes with a diagonal. Likely days he's been here, or solo ping-pong victories. Locke asks how long Desmond's been here. "Shut it!" That's how long!