PokéBase - Pokémon Q&A
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If the Pokémon Is transfered from Bank to Home to Sword/Shield, does it gain the experience boost? If so, how much by?

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Go check out this chart on Bulbapedia. Likely, your 3DS and Switch/Mobile Trainer ID and Secret Trainer ID are not the same, so a Pokemon transfered from Bank ---> Home ---> LGPE/SwSh would gain the 50% experience boost.

Any traded Pokemon will receive 1.5x the normal experience while foreign Pokemon will receive 1.7x the normal exp.

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