You will need to make a claim with your comprehensive portion of your physical damage insurance coverage since your car was stolen, hopefully you called the police and had a report made. Having a police report should help with the claim process with both your primary insurer and your GAP insurance carrier.

Once the claim is made the insurance company will investigate and let you know if the claim has been accepted or denied. Some insurance policies have terms in them that allow the insurance provider to turn down a claim due to clauses for negligence or not properly safeguarding the vehicle. Usually this means leaving keys in the car (ignition or in plain site normally) and/or not locking up the vehicle. You will need to speak with the claims adjuster on your claim to find out if having the keys locked in your girlfriend's purse in the trunk will hurt your claim since insurance companies' guidelines differ.

As for the GAP insurance and how much it will cover, that will depend upon the terms of your GAP policy. Once you have placed a claim with your comprehensive insurance then you can inform your GAP provider of your stolen vehicle.

Once your primary insurance provider has paid out their portion of the insurance settlement, your GAP coverage should kick in. How long this will take will depend upon state laws but usually needs to be within a "reasonable" amount of time. To find out how long your insurance providers think it will take to settle both claims and get the money to your lien holder, speak to the claims adjusters of both the comprehensive and GAP insurance companies.