I don‘t remember getting a certificate when I got mine. Mine was the fixed brace, prior to the adjustable one they have on them now. However, since the pistol is sold as and registered as a pistol, I wouldn’t think there would be a problem if left unchanged. Since the brace is an SBA, you may want to go to their website and see if they have a letter of compliance. I’d think they would have that since the SBA braces are sold as aftermarket upgrades.
I changed my brace for a Gearhead Works Mod 2 adjustable brace. GW does have a letter of certification on their website for that and I printed it out. I also put a Law Tactical Folder on mine. With the folder, it put me over the 13.5” LOP the BATF has referenced. I emailed Gearhead Works and told them about the LOP and they sent me a stop for the brace which basically eliminates the last stop on the brace and keeps it in compliance (if there is such a thing). They sent it at no charge, which was really nice.