2007 fat boy stopped running without warning. Unable to re-start. Checked battery, battery is fine. No response from ignition. Checked fuses, all good.

Check for things like a bad kill switch, ignition switch, and coil. Clean battery terminals and cable connections--apply dielectric grease. Batteries are always problematic on motorcycles. I would remove the battery and charge it on a motorcycle battery charger or regular battery charger with a ampere damper (1.5 to 2 amps)--then, you'll really know where it stands.

Could be rubber gasket from manifold to carb. If it turns over has fire check carb if its getting too much air it won't crank.