Please try the following steps to search for the Pokémon you have moved from Pokémon Bank to Pokémon HOME.
▼How to Search Pokémon
・Mobile Device Version
1. Start the app and tap the "Pokémon" tab on the upper right corner of the screen.
2. Tap "Search."
3. Tap "Pokémon name" and enter the name of Pokémon you wish to look up.
4. Tap "Search" again to show the result.
・Nintendo Switch Version
1. From the main menu, select "POKÉMON."
2. Select the Pokémon HOME icon.
3. Select "Yes" to dismiss the message: "Do you want to check the Boxes in Pokémon HOME?"
4. Press the X button to open the "POKÉMON LIST" screen.
5. Press the X button to open the "Filters" screen.
6. Select "Pokémon Species" and choose the Pokémon name you wish to look up.
7. Press the B button to show the result.
If you are unable to find the Pokémon by doing the search, please use the Notebook function to check the history of your deposited Pokémon.
▼ How to use Notebook
・Mobile Device Version
1. Start the app and tap your username.
2. Tap the "Notebook" button on the bottom right corner of the screen.
3. Tap a card to check details of a received or deposited Pokémon.
・Nintendo Switch Version
1. From the Main Menu, select "NOTEBOOK."
2. Select "History."
3. Select an entry to check details of a received or deposited Pokémon.
▼ Checking with Notebook
・Please check if you have either deposited, moved or received the Pokémon.
・Check under withdrawals to see if you have withdrawn the Pokémon from Pokémon HOME and moved it to other Pokémon games.
・Check under releases to see if you have released the Pokémon from Pokémon HOME.
Please note that when you move Pokémon from Pokémon Bank to Pokémon HOME, you will also move any Pokédex data unlocked in Pokémon Bank. When that happens, you may be able to see the Pokédex entry for Pokémon that have not been transferred at all. So it is possible for the Pokémon you did not transfer from or store in Pokémon Bank to be registered to the Pokémon HOME Pokédex.
If the Pokémon does not appear as registered on your Pokémon HOME Pokédex, it would mean that you never had that Pokémon in Pokémon HOME.