A lot of people get pistol versions of the AR, AK, SIG and other "black" rifles and put shoulder stocks on them. Much easier than having a full length rifle that has to be cut down, the barrel & gas system's modified and re-tuned, etc. Many people prefer to modify the assault style pistols because there are already rifle versions available with stocks and other parts/accessories that will need little or no modification. Just fill out the Form 1 - it can be downloaded from the BATF web site - send in the $200 fee for the stamp, wait for the paperwork to be returned (as little as 6 weeks or as long as 12 weeks or more) then build your gun.
Essentially, you buy your pistol, get the stamp and add the stock in that order
. DO NOT
modify a gun BEFORE
you complete the paperwork and receive approval from the ATF if you will be making a Class III or AOW classified firearm! If you're caught, you WILL regret it.