Get the timecard from the museum guard, who is at the Clown Store.
You will have to check the various sites for video. There may be some at the related links below.Surveillance Videos on Counterfeit IslandTo watch the video of the theft, get the time card from the museum guard, who is at the Clown Store.
watch all the videos there
Counterfeit IslandNo, Counterfeit Island is real. In fact, it'd be better named as "Art Island".
Go and watch youtube videos.
(There is a link to the video walkthrough on the related question below.)
there is no mansion on counterfeit island
You do not die on Counterfeit Island.
There is no camera as an item on Counterfeit Island.
You can review the surveillance videos once you have the timecard from the museum guard. You can find him at the Clown Store.
You will have to swim for it : the lighthouse is on Big Nate Island, not Counterfeit Island.
you go back on counterfeit island
Get the timecard from the museum guard (captain Happy Foot), who is at the Clown Store trying to cheer himself up. With the card, you can look at the proper time on the videos in the security room, and get a photo of the culprit to show Downtown.