Strengthening the National Instant Criminal Background Check System Act of 2018 This bill reinstates the “Implementation of the NICS Improvement Amendments Act of 2007 ” rule finalized by the Social Security Administration on December 19, 2016. The rule implements a plan to provide to the National Instant Criminal History Background Check System the name of an individual who meets certain criteria, including that benefit payments are made through a representative payee because the individual is determined to be mentally incapable of managing them. (Current law prohibits firearm sale or transfer to and purchase or possession by a person who has been adjudicated as a mental defective.)