Yes, it is possible, provided the institution has either been authorised to do so, or the account holders are using this institution as a payment service provider to process their payments.
Can a non-bank institution move money from one person’s bank account to another person’s bank account?
What are the steps involved in transferring funds between banks?1 ansWhere can I locate the bank-by-mail addresses for major U.S. banks without having to call each institution?1 ansHow long does it take to transfer the money to the bank?1 ansCan the source and destination of a wire transfer be tracked by third parties?1 ans