Okay, you say two different things here. You say your husband can't call, they close at 4:00pm (it's 4:30, incidentally) and so you have to deal with this. Then you say when he calls they say your wait time is blah blah blah..... okay, that's when you call the lines to get in to file a claim. That is not when he directly calls the fraud unit and deals with an issue they're working on.
Okay, then you say you are talking to the director of appeals. Have you asked this person to connect your husband with someone in the fraud unit, or whomever he needs to speak to? Have you asked this person to give you the direct number of someone who can help determine why this happened, what your next step is, who your husband should talk to? In the majority of cases, when there is an unemployment issue to be dealt with, the person has to be present and on the phone, and can then authorize someone else to ask the questions or talk for them if they are not able to deal with it themselves. But they should not give you carte blanche to deal with your husband's affairs just because you call and ask about them.
As I said, I worked in u.i. fraud enforcement, and the wife continuing to certify and getting the benefits after the husband has returned to work was VERY common, especially in cases where husband worked out of town and wife handles all the money issues and bill pays and what all. Teenagers in the home, heck, grandmas in the home have been known to call in and get the benefits after papa went back to work. It only has to stop when papa gets a notice to report in or when he runs out of benefits. You are sure your 8 year old hasn't been doing it, but frankly, your story is going to sound really unlikely.
Having the husband continuing to file weekly certifications and forgetting to tell the wife he was still doing it isn't unusual either. You don't need to get all huffy about it and come up with all these excuses why you alone need to deal with it, cause he can't, cause he's working, either. He's the one who will be prosecuted for fraud if this matter goes a whole lot further without resolution. That should be worth his taking his time to get on it, even if he has to call them from wherever he is on his lunch break or whenever he can. He probably, due to the nature of his work, relies on his unemployment benefits each year when he's out of work seasonally, and if they are messed up and there are issues, he will not get any more of them until these issues are resolved.
He needs to be getting with the agency to fix this. You do not need to be on a message board asking for general advice from people in other states, who are generally unfamiliar with unemployment insurance even if they are attorneys, and who, even if they are very well based in TN unemployment, as I am, are unable to research your particular situation, hoping, I guess that they'll tell you something besides that you need to let your husband work with the agency. Hiring an attorney to represent your husband would not be worth it, and would not help one iota, as this will be resolved within the agency, and they will be able to see exactly what has happened and will be able to determine whether or not fraud has occurred.
If there have been checks issued, and cashed, rest assured, they can tell exactly when they were cashed, where they were cashed and who signed the checks. They can tell exactly when the certifications were made to receive benefits, day hour and from which computer or telephone. They can tell when money was put on a debit card and when and where it was taken off. If no money was put on there, no certifications were made for these weeks, then they can tell that, too.
And they'll be glad to help him resolve the situation, though as it has been said, this is a one in a trillion billion chances that the system somehow just spontaneously decided to override itself and issue weekly benefits to a claimant who'd stopped certifying for benefits weekly, and also glitched to the point that it failed to put this erroneously paid money into his debit card account or send him a check for benefits.
What stops the benefits from coming when a claimant returns to work is not that they call and tell the unemployment system they've gone back to work, or that their employer calls and reports they're working. What stops the benefits from coming is that the system receives no more of the weekly certifications for benefits. The certification is what generates a payment. How it happened that your husband's certifications just kept being made and money kept being paid to him without showing up in your account or your mailbox is something he'll have to work with the agency to figure out.