Is a cop without an FFL allowed to bring his handgun into a liquor store?

Not sure what you are asking. In relation to guns, FFL stands for Federal Firearms License, which is a license to sell handguns, and generally speaking, has nothing to do with being a police officer. That said, in the U.S. police officers can carry a handgun just about anywhere, especially if it is while discharging official duty, or while on duty. Also, under federal law HR218, police officers can carry almost anywhere in the U.S. even when they aren't in their home state, but they must abide by local restrictions.