Strictly speaking the money you are wed would still be the responsibility of the customer. Whether they paid it to someone else is not really your problem, unless you were at fault for these different details being sent out. So if you had given them the wrong bank details or had left your emails and servers negligently open for others to access then you could be at fault. However, if this was the work of professional hackers and there is nothing you could have really done to prevent it then by not being at fault the other side should still pay you.
They have been the victims of fraud and if that was the case it does not mean that they no longer have any responsibility towards you.
If you want to take this further, whenever a dispute arises over money owed by one party to another, the debtor can be pursued through the civil courts for recovery of the debt. As legal action should always be seen as a last resort, there are certain actions that should be taken initially to try and resolve this matter informally and without having to involve the courts. It is recommended that the process follows these steps:
1. Reminder letter – if no reminders have been sent yet, one should be sent first to allow the debtor to voluntarily pay what is due.
2. Letter before action – if informal reminders have been sent but these have been ignored, the debtor must be sent a formal letter asking them to repay the debt, or at least make arrangements for its repayment, within a specified period of time. A reasonable period to demand a response by would be 10 days. They should be advised that if they fail to do contact you in order to resolve this matter, formal legal proceedings will be commenced to recover the debt. This letter serves as a ‘final warning’ and gives the other side the opportunity to resolve this matter without the need for legal action.
3. Before you consider starting legal action you may wish to consider sending a formal statutory demand. This is a legal request which asks the debtor to pay the outstanding debt within 21 days and failure to do so will allow you to bankrupt the debtor (if they are an individual ) or wind up the company (if they are a business). For the relevant forms to serve a statutory demand see here: https://www.gov.uk/statutory-demands/forms-to-issue-a-statutory-demand
4. If you wish to go down the legal route instead of a statutory demand, a claim can be commenced online by going to www.moneyclaim.gov.uk. Once the claim form is completed it will be sent to the debtor and they will have a limited time to defend it. If they are aware legal proceedings have commenced it could also prompt them to reconsider their position and perhaps force them to contact you to try and resolve this.
Whatever correspondence is sent, it is always advisable to keep copies and use recorded delivery so that there is proof of delivery and a paper trail. The court may need to refer to these if it gets that far.