1. You need a "virgin" lower that has never had a buttstock or a lower that is specifically marked as a pistol lower.
2. Just owning the short upper and having it in the same house as a full size AR without owning a pistol lower is enough to classify you as having illegally manufacturing an SBR in the eyes of the ATF. As an example if you own a glock and buy one of those KPOS stock kits, even if you NEVER ASSEMBLE IT the ATF still says you built an SBR and NFA rules apply/if you get caught you're going to jail.
That seems crazy... what about gun stores... if they store lowers and uppers in the building are they officially SBRs?