Direct transfer is impossible. GBA cartridges (LeafGreen) and DS cartridges use incompatible hardware/protocols. No official link cable or software exists.
Tools like PKHeX can extract .pk3 files from a LeafGreen save (via emulator/flashcart) and inject into modern saves. Requires CFW/PC. Not "legit" for online play.
Best advice: Find a friend with a DS Lite + Gen 4/5 cart + 3DS + Bank already installed. Or replay the experience in a modern game.