It actually is more complicated when we don't involve B/W/B2/W2 and we're just transferring between X/Y games, a cart and a download title.
If SHE has the download X/Y, and HE has the cartridge and the Pokemon are on HER Pokebank, it's simple, just put his cartridge on her 3DS and use Pokemon Bank.
Now, if HE has the download X/Y, and SHE has the cartridge and the Pokemon are on HER Pokebank, the only way to transfer is if he starts his own Pokebank. She would download the Pokemon from her bank to her cart, then she'd put her cart into his 3ds and upload the Pokemon to his bank, then he can transfer the pokemon from his bank to his downloaded X/Y game.
Is the free trial of Bank still available? Or is this $5 the guy needs shell out?