Some monsters can be teleported to another island when they reach level 15. When a monster is teleported, it permanently leaves the island it was born on and is moved to the new island, turning back into an egg and going into the empty Incubator on the destination island. This also resets the monster's level down to 1.
At present, this process cannot be reversed. That is, after a monster is teleported to another island, it can't be returned to its original home.
Teleporting may also change a monster's breeding and incubation times, as the the destination islands have different features than the ones of the home islands, and may enable other characteristics not available on the monster's birthplace.
Ethereal Island Monsters
Ethereal Monsters of a single element can only reach Ethereal Island through teleportation from their other islands.
~ Error message when trying to buy a Single-Element Ethereal via an Ethereal Island monster's "Like" tab
Gold Island is different from both Ethereal Island and Shugabush Island; monsters are not teleported to it. When any of the monsters (not including ethereal monsters) from Plant Island, Cold Island, Air Island, Water Island, or Earth Island reach level 15, that monster appears in a list of monsters on Gold Island. Those monsters can be placed on the island. Placing a monster on Gold Island does NOT remove the monster from the original island. The monster on Gold Island is like a "trophy copy" of a monster that's living on one of the natural islands.
If you have a level 15 monster that you have placed on Gold Island, and then you later teleport the same monster to Shugabush Island, the monster will vanish from the original island it was from and from Gold Island.
Alterations in Breeding Mechanics
As the monsters' breeding capabilities may be altered after Teleportation, one may not be able to use the same breeding combinations available on the natural islands to obtain a rare monster. For example, on Cold Island, you can breed a Furcorn and a Quibble to get a Deedge. However, after the Furcorn and Quibble are teleported to Shugabush Island, they cannot be bred together; all breeding combinations on Shugabush Island must include a Shugabush monster. A Deedge must either be fed to Level 15 on Cold Island and teleported, or obtained from a failed Shugavox breeding.
The same change does not occur in Ethereal Island, since the Ethereal monsters can't be used for breeding on their original islands in the first place.
Monsters living on Shugabush Island can't be teleported to other islands even after they reach level 15.
Rare Monsters can also be teleported, exactly like normal monsters.