The AR-15 Pistol, Photo Courtesy of Thordsen Customs
Thanks to 
The venerable AR-15 platform is a civilian adaptation of the M16 rifle, which first saw service during the Vietnam War. The current lighter and shorter generation is referred to as the M4 carbine. src The M16 was the rifle I first qualified on in the Air Force, and I had a 2-week temporary assignment cleaning them in an armory, so I have a special affinity for the robustness of this platform.
The Lower Receiver
Image Courtesy of Palmetto State Armory
The lower receiver is where the trigger assembly lives, the magazine well, and is the platform atop which the rest of the rifle is built. It is important when choosing one, that it be MIL-SPEC. This means it was built to military specifications, and can easily be mated with other MIL-SPEC components from other manufacturers. When ordering and shipping to a firearms dealer, I came to learn that these lower receivers were classified as pistols, so the laws applying to pistols applied to them. The reason for this is that an AR-15 lower can be built into an AR-15 pistol!
Complicated Laws
The laws surrounding AR-15 pistols are complicated, and failing to follow them by the letter can cause you to wind up in jail. First off, you should have a good understanding of how US law defines different types of weapons. The most relevant are handgun(pistol), rifle, short-barreled rifle, and any other weapon(AOW).
Rifle US Code 18 U.S.C., § 921(A)(7)
The term “rifle” means a weapon designed or redesigned, made or remade, and intended to be fired from the shoulder and designed or redesigned and made or remade to use the energy of an explosive to fire only a single projectile through a rifled bore for each single pull of the trigger.
Handgun (Pistol) US Code 18 U.S.C., § 921(A)(29)
The term “handgun” means— a firearm which has a short stock and is designed to be held and fired by the use of a single hand
Short-barreled Rifle (SBR) US Code 18 U.S.C., § 921(A)(8)
The term “short-barreled rifle” means a rifle having one or more barrels less than sixteen inches in length and any weapon made from a rifle (whether by alteration, modification, or otherwise) if such weapon, as modified, has an overall length of less than twenty-six inches.
Any Other Weapon (AOW) US Code 26 U.S.C. § 5845(e)
The term “any other weapon” means any weapon or device capable of being concealed on the person from which a shot can be discharged through the energy of an explosive, a pistol or revolver having a barrel with a smooth bore designed or redesigned to fire a fixed shotgun shell, weapons with combination shotgun and rifle barrels 12 inches or more, less than 18 inches in length, from which only a single discharge can be made from either barrel without manual reloading, and shall include any such weapon which may be readily restored to fire.
Now that we have defined various associated weapon types, we must ensure our AR-15 pistol does not accidentally fall into the realm of Short-barreled Rifle (SBR), or Any Other Weapon (AOW). Our pistol can later be turned into a rifle, but more on that later.
The SBR Trap
First off, by definition, a pistol cannot be fired from the shoulder using a stock, which would cause it to fall under the category of SBR according to the National Firearms Act(NFA). src While SBRs can be obtained legally through a costly application and purchase of a NFA tax stamp, it also causes it to become a controlled item, and placed into a permanent registry. Owning an SBR without purchasing a tax stamp, is considered a felony punishable by fines and imprisonment. So we know at this point, we can never install a shoulder stock onto our AR-15 pistol, or risk legal trouble.
The AOW Trap
For being classified as an AOW, let's quote the ATF directly:
ATF has long held that by installing a vertical fore grip on a handgun, the handgun is no longer designed to be held and fired by the use of a single hand. Therefore, if individuals install a vertical fore grip on a handgun, they are “making” a firearm requiring registration with ATF’s NFA Branch. Making an unregistered “AOW” is punishable by a fine and 10 years imprisonment. src
So basically here, the ATF is telling us that mounting a vertical foregrip to an AR-15 pistol, classifies it as neither a pistol, or rifle, but an AOW, which must be registered in the same way an SBR is.
The Ugly Buffer Tube
Image Courtesy of CBC Industries
As you can see in this image, a tube is attached to the lower which contains a spring that is vital to the operation of the weapon. In addition to being rather ugly, a simple tube doesn't provide much functionality and benefit. Several manufacturers have designed different solutions, including wrist braces, blades, and other furniture designed specifically not to be a shoulder stock.
Image Courtesy of Thordsen Customs
The device I like is the cheek rest manufactured by Thordsen Customs pictured above. I decided to research the legality of this device. On the manufacturer's website they link both their letter to the ATF requesting approval, along with the ATFs response including the snip below.
FTISB's evaluation of the submitted items consequently finds the attachment of the stock
"saddle" to an AR-t1pe pistol would not change the classification of the pistol to an SBR.
Our Branch fuilher notes that as long as the saddle device as evaluated and installed to an
AR-t1pe pistol, is not designed or redesigned and intended to contact the shoulder and is
not used as a shoulder stock, its possession and use would not be prohibited.
ref:https://www.thordsencustoms.com/pub/media/wysiwyg/ATF_Response_letter_for_AR_pistol_pack.PDF
ref: https://www.thordsencustoms.com/ar-ak-enhanced-pistol-cheek-rest-kit-w-mft-saddle-black/.html
So when it comes to government, if there can be any doubt, it's better to protect yourself. And despite the possibility of shouldering a device, it might be a really bad idea to do so.
What about a foregrip?
So we've already learned that a vertical foregrip on an AR-15 Pistol is a big no-no. Is there anything else we can do? You bet, we can install an angled foregrip, because by definition, something at an angle is not vertical. Below is an example of an angled foregrip:
Just like with our buffer tube furniture, anything that can be questioned, should be documented. I found an ATF letter covering angled foregrips as well, which is good example to share regarding what these letters look like.
Converting AR-15s
As promised, let's look at what the ATF says about conversions of AR-15s.
Can you make a rifle into a pistol?
No. A firearm that was originally a rifle would be classified as a “weapon made from a rifle” if it has either a barrel less than 16 inches in length or an overall length of less than 26 inches. If an individual wishes to make an NFA firearm,
https://www.atf.gov/firearms/qa/can-i-lawfully-make-rifle-pistol-without-registering-firearm
Can you make a pistol into a rifle?
Assuming that the firearm was originally a pistol, the resulting firearm, with an attached shoulder stock, is not an NFA firearm if it has a barrel of 16 inches or more in length.
https://www.atf.gov/firearms/qa/can-i-lawfully-make-pistol-rifle-without-registering-firearm
Can you convert a pistol into a rifle, and then back to a pistol again?
Yes, according to ATF Ruling 2011-4
The moral of the story here, is if you want to convert something back and forth, you should first buy a pistol, and later buy the parts to convert it to a rifle. This may not be the smartest way to go, because if your actions are ever interpreted as attempting to build an SBR, it could land you in some serious hot water!
Can an AR-15 pistol be concealed?
Surprisingly, because it is classified as a pistol, if concealed carry of pistols are legal in your jurisdiction inherently or through a permit, you would also be able to conceal this. NOTE: Please check the laws of your local jurisdiction before assuming anything is legal.
Thanks for reading. It's great to have the opportunity to document my prior research on this subject, and hope it may be useful to someone in the near future. Please be sure to check your local laws, and check them often, because laws are subject to change.