Firearms Checks (NICS)
https://www.fbi.gov/how-we-can-help-you/need-an-fbi-service-or-more-information/nics
Voluntary Appeal File Application
https://www.fbi.gov/file-repository/vaf-form-25.pdf/view
NICS Guide for Appealing a Firearm Transfer (denial)
https://ucr.fbi.gov/nics/appeals/nics-guide-for-appealing
Firearm-Related Challenge (Appeal) and Voluntary Appeal File (VAF)
https://www.fbi.gov/how-we-can-help-you/need-an-fbi-service-or-more-information/nics/national-instant-criminal-background-check-system-nics-appeals-vaf