Tell can safely tell your brother that the moon isn't a hologram, because the video is a HOAX. Holograms simply don't work that way.
See how easy that is?
For a more technical argument:
Holograms aren't free floating images like you see in the movies - they are images stored on a medium (hereinafter referred to as "film"). Recording a hologram requires the use of a pair of lasers to illuminate the object and then be recorded on the film. Viewing the hologram afterwards requires illuminating the film with a laser - you can't see it by holding it in the sun, which is to say that a hologram of the moon therefore WOULDN'T be visible even if there were such a film in place, because the light from the sun would show the film rather than any hologram that might have been imaged on it.
** the "hologram" on your credit card doesn't require a laser to see it because it isn't actually a hologram - it is a multi-layer image, each layer of which can only be seen from a narrow angle, resulting in different layers being visible as the angle to the card changes. It does, however, still require a solid surface to work.
Mike