Your policy most likely provides that you must report the incident "promptly", so i would do so. Any of the other issues about licensing etc. would only be made worse if you don't report it and lose coverage as a result. If you folks get sued, then the insurance company should defend you and the hired attorney should be able to address these other points.
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Call your own insurance company to report the accident as soon as possible. If you don't report within a certain number of days after the date of accident (per your policy), the company has the right to disclaim and won't cover you or any claim made by the "other person". Most insurance companies, including GEICO, have 24 hour claim reporting services. Also, if you do not have collision, call the other vehicle's insurance company to report property damage (property damage only).
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You can still call the insurance company and report the accident. Geico will not deny coverage for the four day delay. They might not even ask if your husband is licensed, but if they find out, don't be surprised if you need a new insurance company.
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