What does "trying to sue him" mean? She has either filed a lawsuit, or has not. You also did not tell us what the charge were for? What did your boyfriend use the cards for? One obvious solution is that your boyfriend owns up to his responsibilities and reimburses his ex for his use of the cards. The two of them can try to agree on a number, in writing, and he pays it. If she does not use the money to pay her credit card it is then her problem (and not an excuse for him not to pay). If he does not want to pay for his charges, it is probably not a good sign for the future. Otherwise, if she sues him he'll have to defend.
I would say that she probably has a valid claim. He promised to reimburse her for his use of her card. He used the card. So there is probably a valid and enforceable oral contract. He didn't repay, or did only partially. So there is a breach of contract. He may have defenses (Statute of Frauds, laches, statute of limitations, etc.), so he should consult counsel.
So if he uses her credit, promises to pay, but never follows through, what do you think he will do to you? Leopards don't change their spots and you never really know someone until you break up with them. Seriously! Sure she can sue him for borrowing her credit cards & running up debts in her name! Hope this perspective helps!
Technically, yes, the ex can sue your boyfriend for debts he ran up as a user on her card. A written agreement isn't necessary to form a contract (obviously, it helps). But, she'll have to prove there was some kind of agreement for him to pay the debt and that it wasn't merely a gift. Your boyfriend's statements on social media don't help his case. Your current financial status is irrelevant to liability - he probably owes the money. Whether the ex can collect - that's another issue.
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