Never had this issue come up before. However, if you can get to the pawn broker's insurance company you should file a claim first and see if they will accept the claim.
The one problem you may have with suing the pawnshop is whether they can be held liable for an intervening crimminal act. We have had this issue come up before and the court found that a company such as the pawnbroker in your case cannot be held liable for crimminal conduct unless it was forseeable that the crimminal conduct would likely occur.
Start with the insurance company. Also ask the pawnbroker owner for information on how to proceed. He may be able to help.
Under Florida law, you can send a statutory insurance demand to the pawn shop, advising of your claim and asking for a copy of its insurance policy. The pawn shop is required to provide you with a copy of the policy. After you obtain a copy of the policy, you can review the terms to determine if there's an argument for coverage of your claim. Even if the insurance policy does not cover your loss, there may be additional legal arguments for why the pawn shop should be liable for the theft, but more information is needed to evaluate the matter.