Gaming Pokebank pass transfer

[Fender94]

I would like to use Pokebank to transfer Pokemon from Y to Omega Ruby. The problem is, I have a Pokebank pass on the 3DS that I can't update. I have another 3DS that is on 9.4, am I able to use the Pokebank pass/account on the newer 3DS to avoid re-buying the pass? Or is it locked per console?

Thanks!