It's better to be frank with his father. If you really can't borrow it, you can only negotiate the repayment, and if you can't negotiate, you will pay back some money every month. The bank says that it is bluffing to sue, and credit card arrears generally do not constitute criminal responsibility (unless it is malicious failure to repay, debt evasion and providing false materials). It is just a civil dispute. Even if you sue the court, you show your willingness to repay but you don't have money now, the court will coordinate and deal with it first.
Also, if your boyfriend can't use a credit card, don't touch it. With this money, if you apply for a monthly installment or a minimum payment, the bank won't bother your boyfriend. If you don't pay back any money, or even fail to meet the minimum repayment requirements, it will be several months before the bank will collect debts.