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First, you should see if the debt is barred by the statute of limitations. In Connecticut, the SOL is 6 years from the last charge or payment on the account. If the debt is barred, nothing else matters, and her response should be that the debt is barred from collection.
If the SOL is not helpful, the rule is that authorized users are not responsible or liable for debt they have not contractually obligated themselves to pay. This is a sticky point right now. Creditors and credit bureaus are routinely reporting accounts for consumers who are authorized users. This is a violation of the letter of the law.
If this is the case, you should respond to the suit by stating that she never agreed to pay the debt and demand that they produce an original contract, with her signature, which proves her liability for this debt. If they are unable to prove her liability, she can request case be removed.
If she signed up, they can probably hold her to it. Also, if there is no documentation about her being released, you're not going to get anywhere with arguing that. It will be a swearing match between you and the creditor, and it is not likely that the judge is going to rule in your favor if you don't have some proof - other than your testimony.
If the debt is not barred by the SOL, the creditor is likely within its rights to sue her.