If you are able to find a Pokémon that has been transported from Pokémon GO in the Smartphone version of Pokémon HOME but cannot find it in the Nintendo Switch version, the Nintendo Account linked to the Nintendo Switch version and the one linked to the Smartphone version are different.
Please start Pokémon HOME using the same Nintendo Account that is linked to your Smartphone version of the app.
If you are using the Basic Plan of Pokémon HOME, you can check which Nintendo Account it is linked to using the steps outlined below.
▼How Confirm Nintendo Account on Smartphone Version of Pokémon HOME
1. Start the app and tap the Menu button in the middle of the screen.
2. Tap Options > "Changing your Nintendo Account" > "View details."
3. Read the precautions, then tap "Change Nintendo Account" followed by "Yes."
4. Once the page for the linked Nintendo Account appears, please check the Username or email address to confirm the linked Nintendo Account.