This section is incomplete. Please feel free to edit this section to add missing information and complete it. Reason: Check if the Everstone is received if the player shows any OT Togepi / Togetic / Togekiss (not necessarily the one from the Mystery Egg)
Mr. Pokémon asks the player to bring the Mystery Egg to Professor Elm for study, due to his expertise on Pokémon Evolution. After the player defeats Falkner and obtains the Zephyr Badge, Elm's aide will return the egg to the player, revealing that it is in fact a Pokémon Egg. The Egg, if the player chooses to keep it in their party, will eventually hatch into a Togepi. If the player shows the hatched Togepi to Professor Elm, he will give the player an Everstone.
When this item is received from Mr. Pokémon, the last Pokémon Center used is set to Cherrygrove City. Therefore, if the player blacks out or uses Teleport outside of battle (even though this move is not yet legitimately available), they will go to this Pokémon Center instead of going directly to their house and skipping the first battle against the rival.