Schengen does not have anything to do with money transfer. Schengen is about the open borders for persons and the check of documents when you enter the Schengen space, a Non-Schengen state has to have a secured border with the Schengen group and a secured border to the outskirts of the EU.

In the EU you have the SEPA system which applies to all EU members, so all banks use the same contructions of accounts and transfers(IBAN-code + BIC/SWIFT-code). It is the same problem if I would transfer this amount of money in German space or Romanian space without telling the bank for what I used it.