Please be take notice that it is considered insurance fraud to file false insurance claims in an effort to secure coverage. You should never falsify dates of car accidents and then report such information to your insurance company.

You are also not allowed to enter into an unlawful agreement with the other party to attempt to defraud your insurance carrier. If your insurance policy was cancelled on the date of the accident, then you would be deemed uninsured on that date.

Under any circumstances, you would ultimately be liable for the damages which were sustained as a result of your negligence.

I would urge you to determine why your former coverage lapsed. If it was, as you say "lapsed and canceled without [your] knowledge" it is always possible that the notice of lapse and cancellation was never issued or was defective.

Depending on the facts and circumstances (especially the timing), an insurance company's failure to provide proper notice could mean that your former policy would still be deemed to have been "in force" as of the date you had the accident, and your former insurance company would thus remain liable. It may be a long shot, but it is the only shot.

As you are in the military -- and thank you for your service -- you should consult with your unit's legal assistance officer for assistance. There may even be some special rules that apply to the form of notice required when the insured is on active military duty which a lawyer in the service would be more likely than a civilian lawyer to be aware of.

Even if you ultimately learn your old coverage had been properly canceled and thus you had no insurance, the military lawyer may also be willing to advise you how you might negotiate down or settle with the other vehicle owner (or his insurance company) for a lower amount of damages, and also can advise you as to whether if the other side were to sue and get a judgment against you, how much could be collected and your alternatives. Or the military lawyer may refer you to a civilian lawyer who has the answers yet would be reasonably priced.

As the previous answer states, do NOT even think of engaging in insurance fraud. You had a collision. Don't even think of engaging in collusion. Insurance fraud is not only a crime, but a dishonor to you and the military. So consider yourself lucky that you're only facing the costs of repairing the vehicle you hit, and not a dishonorable discharge plus several years in jail.