So B should have gotten the funds, but A did to a BS account which apparently doesn’t exist.

You can 100% escalate with the party that got the funds, if you have an actual account with provider A go in with that information and then bring up the fact that you made a payment in error. If you don’t have an account with provider A then it will be more difficult but it’s doable.

It’s tough if you use the “wrong” terminology or get someone who just doesn’t get it. Explain to the first person you speak to that you sent funds to them, and there was a mix up with the account numbers. Ask for their help in finding out where the funds went so that you are able to coordinate with your bank - come at it with a very calm “Im really hoping you can make an exception and help me” approach. When they try to tell you the account doesn’t exist ask them to bring in their supervisor, and go at it again with them.

Ask them to log a ticket internally to track the funds, they definitely have a way to do that you just have to stick with it and keep escalating, ask the customer service rep to speak to billing for you.

Sorry for the long reply