Protecting Americans from Gun Violence Act of 2022 This bill establishes provisions related to firearms, including with respect to gun violence research and the reporting of lost or stolen firearms. Among its provisions, the bill establishes a fee for firearms-related background checks under the National Instant Criminal Background Check System, directs the Centers for Disease Control and Prevention to conduct or support gun violence research, requires a gun owner to report a lost or stolen firearm to local law enforcement authorities within 48 hours of discovery, and establishes penalties for violations of the bill.