Don holds it during the segment and opens it and reads her signature when he needs to be reassured that the last few minutes actually happened. It takes a bit of time for it to sink in. Mac keeps glancing over at him with that look that means they are both going to explain what just happened to her and Will as soon as possible, which means it must have been real.
The next time he can leave the control room he takes the book to his office and puts it in his bottom desk drawer where he's been keeping the fake copy. He takes the fake out of the drawer and writes out a post-it that says, "Whatever Sloan has you doing you can stop now. It was me by the way. -Don." He sticks the post-it on the cover, over the title, and takes it out into the newsroom. Neil is gone from his desk which makes this much easier for him, no explanation needed, he just leaves the copy under Neil's keyboard and walks away.
The segment is over now and Will passes him while heading toward his office. He spots Sloan walking hesitantly toward him. He's leaning against a desk now and when she reaches him she stops a few feet away and smiles. "When tonight's over we should talk," she says. He knows this and desperately wants to have that conversation. He answers, while leaning in toward her, "Yeah, we really should."
She moves to leave but before she can pass him he takes her hand and squeezes it tenderly three times. "No professor, you get to watch me walk away this time," he says, almost directly into her ear. After her spectacular exit earlier he feels she needs to understand what he felt in that moment. She seems to immediately understand his request and stares at him while she nods her head once. He squeezes her hand one more time and turns around and walks away from the one person he really wants to be close to right now. He hopes that this is how she felt earlier.
When he gets to the door to his office, in the reflection, he can still see her watching him.