(Story) to Unlock The Mystery Gift Option – Pokémon (BDSP)
To unlock the mystery gift, follow the steps.
Go to the 3rd floor of the TV station tower in Jubilife city after defeating the first gym leader and beating the double battle in route 204.
Now talk to the NPC.
Select, Yes.
Now select, Everyone Happy wifi connection.
Now, you'll get the Mystery Gift.
You can see the Mystery Gift now.
Select "Get via Internet".
You'll now be connected to the internet, Press "Yes".