Federal Firearms Licensee Protection Act This bill amends the federal criminal code to modify provisions related to theft of firearms. Under current law, it is unlawful to steal a firearm from a licensed importer, manufacturer, or dealer, or from their business premises. This bill broadens the scope of unlawful conduct to also prohibit stealing a firearm from a gun range that rents firearms or a shooting club. Additionally, the bill modifies criminal penalties for an offense: to increase from 10 to 20 years the maximum prison term, and to create a 3- or 5-year mandatory minimum prison term for an offense that occurs during the commission of a burglary or robbery. Finally, an attempt to commit an offense is subject to the same penalties as a substantive offense.