What gift does R bestow upon the old man in Chapter 16 and what hopes does R have for the present?

For the old man's birthday, R gives him an exquisitely-crafted music box. Since music boxes have already been disappeared, the old man and the narrator are unable to truly engage with it. R explains that he hopes that if the old man listens to the music box once a day, he will slowly regain his ability to remember and experience previously-disappeared objects.