The Teleporter is a device that Henry uses in all of his games, and it often leads him to fail. The only time when he used it correctly was in Stealing the Diamond. The teleporter even appeared in the first PuffballsUnited game, the precursor to the Henry Stickmin series, Crossing the Pit.
When Henry gets near the bank wall, he activates the teleporter, but then he gets teleported into the wall itself, promptly getting stuck until (according to Henry's file photos in Infiltrating the Airship) the chunk of wall he was encased in was mined out by authorities.
Henry activates the teleporter and teleports himself to a shooting practice range. Right at that moment, a policeman opens fire and he shoots Henry by accident, leading to a fail.
During the trial, teleporter appears as evidence which Phoenix Wright can present, but it leads to a fail, being one of "joke items" that Phoenix presents and that prove nothing.
Stealing the Diamond (Win)
In the sneaky path, Henry uses the teleporter and teleports himself to the museum roof. This is the only time that the teleporter actually works for Henry.
Henry activates the teleporter device and white flashes come on. After that he ends in a huge white void where nothing is present (except oxygen, apparently), leading to a fail. The teleporter also turns off, making it impossible to escape.
This is likely a reference to the Spongebob Squarepants episode SB-129, where Squidward uses a time machine, only to eventually get stuck in Nowhere, an infinite white dimension of almost complete nothingness.
Henry uses the teleporter to try to escape from his prison cell. He is teleported to a purple planet from the Starcraft universe, where he appears among a group of Protoss Zealots who are promptly killed by an enemy Protoss Colossus.