Protecting Our Communities Act This expands the types of parts, weapons, and devices that are subject to regulation under federal firearms laws. The bill also establishes a notification requirement following a firearms-related background check that results in a denial. Specifically, the bill includes as a firearm any combination of parts designed or intended to be used to convert a device into a firearm and from which a firearm may be readily assembled; adds armor-piercing, concealable weapons to the list of firearms subject to regulation under federal firearms laws; and provides statutory authority for the regulation issued by the Bureau of Alcohol, Tobacco, Firearms and Explosives to classify bump-stock devices as machine guns for the purposes of federal firearms laws. Additionally, the bill requires the Department of Justice to notify state and local law enforcement authorities following a firearms-related background check that results in a denial.