Point being you cant take your stocked 16" rifle and remove the stock and install short upper. That receiver cannot have begun its life as a rifle. It must have started as a pistol.
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Short answer, no, you can't do what you just told us was an illegal conversion.
There is also the real world case of a fireman who was carrying both an AR rifle and a pistol broken down in the same case, who left it in his vehicle, which was searched and siezed by the cops (for safekeeping as the vehicle was getting towed) who then put the weapons bag in the evidence room where police assembled it into an illegal configuration, sending photos of it to the ATF, who then prosecuted him. He lost because of a bad lawyer and last I heard is still appealing it.
All because of some rivalry with the cops. One in ten thousand odds or even worse, but there it is. Which is why so many of us just build a separate pistol with pistol buffer tube and separate carbine.
These things are so dirt cheap right now giving up an expensive phone plan and spending the dough on parts will build you both in one year. Think about it. I have a PAYG minutes phone that costs me less than $100 a year - not $100 a month - that leaves $900 on the table. You can buy completed AR15's under $400 now. I did it when either would cost you over $650.
It's a fantasy to think you will swap them around anyway, each has its specific application and as you push them toward their best configuration it pretty much voids using it the other way. A pistol lower isn't a good foundation for a good overall rifle - compromise sets in and you find yourself limited in things like grips, triggers, mag releases, ambi controls, etc as the best for one eliminates the best for the other in a lot of situations.
Goof up the assembly process at a range in public and you may well have some idiot take a pic of your mistake to your very considerable regret. Not having that happen and making sure of it is much safer - plus you get two working guns instead of a bunch of leftover parts not earning their keep and being a risk factor.
It boils down to just because you can doesn't mean you should. And the track record of the ATF also means it's only a temporary situation, things can very well change again. At one point a pistol could have a stock on it pinned to the shortest length, but not now. All those pistols had to be reworked at the owners expense.