Since the policy was active from August 31 through September 22, your son will be responsible to pay the premium on the policy. Every company has different rules and guidelines so there may be a fee for canceling the policy before the term is over.
Since you no longer have possession of the vehicle then technically you could cancel your policy. It's important to keep in mind, though, that if you have been continuously insured for 6 months or more you will lose a discount if your policy cancels.
The state of Florida requires that insurance companies refund at least 90% of the unearned premium paid by a customer if they receive a request to cancel. There are instances where a company may include the policies fees within the first month so your refund can vary depending on which company you're with.
After your insurance provider is made aware of any damage caused to your vehicle it will be documented. That being said, if you are using uninsured motorist coverage for the claim, meaning the other driver was at fault but didn't have insurance, you shouldn't have to worry about an increase in your rate since you aren't at fault.