How to transfer Pokémon from XD Gale of Darkness to modern titles, if possible?

[Jyu_Sparktale]

I managed to get my modded Wii U to run XD Gale of Darkness, and I’m wondering if I could somehow transfer the Pokémon from there into the core games.

 

[Nukatha]

Without save editing, no.
To transfer them to Home officially, you need to first trade them to a gen 3 game using a GBA-GC link cable, which is only possible on GC or Wii (the USB GC adapter actually lacks an important data pin in the connector, and thus no homebrew will ever be able to make it work).
From there, transfer to Gen 4 with the slot 2 transfer feature, transfer to gen 5 with two DS systems, and then use the 3DS PokeTransporter feature (which now works without a subscription) to put them into Bank (which also works) and finally, link your Bank to your Home account.