No experience like yours.
I would not send the drivers license. They could be the criminal.
They may have picked his name from a phone book and know nothing more about him.
To be safe you can freeze your credit reports at the three major credit agencies. With the police report I do not think there will be a charge. Also age may exempt from a charge.
Go onto CreditKarma
https://www.creditkarma.com/ and sign up. This is safe. It will give you a reading of your credit each time you log in. I think they will also notify you of new accounts being opened. Look to see when the last credit check was made. It should be by the company that sent the contract. I will bet it is not. The service is free.
You can get free credit reports here
https://www.annualcreditreport.com/index.action Just be careful not to sign up for any of the services they try and sell you. Again look to see if the company has checked your credit.