First of all, we need to determine what laws this new hybrid gun falls under. We got a normal shotgun, which in itself might be under the National Firearms Act (NFA) a Class 3 Destructive device, but most aren't. So, let's assume "Shotzooka" is a standard Remington 870.
Because Billy wants his gun to be more compact, he shortens the gun with a telescopic stock. Great, there are 2 options for that: a full stock that can be lengthened and one that is pretty much folding out completely. This can be a problem if the total gun in its shortest configuration gets below 26 inches length - then it is illegal under Texas law as a short barrel firearm. And the complete removal makes it no longer a shotgun under federal law but pushes it to a different weapon category: Any Other Weapon. Since it once was a proper shotgun (which means it had a stock) it can't ever become a Pistol Grip Firearm.
Now, here comes the crux: owning and operating these is totally fine if you have them registered at the Bureau of Alcohol Tabacco and Firearms. But you need to register your intent to manufacture them before you start with the conversion and have the approval of your project. It also costs 200$ tax -but you need to also make sure your new gun is allowed locally (see below).
The Laser sight likely isn't a problem... but now comes the really big problem:
The laser-guided anti-tank missile. THAT is a problem. Because anti-tank weapons are explosive and all explosives are classed as Destructive Devices under the NFA (well,technically that's Title II of the Gun Control Act of 1968 amending the NFA of 1934...). And possession of such a Title II weapon like a Destructive Devices demands them to be registered and tax-stamoed for 200$ federally - and manufacturing them is prohibited for private citizens.
This means in the act of mounting the missile to his shotzooka he turned her into an illegal, unregisterable NFA Class3 DD of the explosive type, illegally manufactured it, and just for the possession alone put himself up to a fine of 250k and 10 years jail time:
The charge of unlawful possession of a destructive device in violation of the National Firearms Act carries a maximum statutory penalty of 10 years in federal prison and a $250,000 fine.
But the trouble doesn't stop there, Texas itself has a penal code that defines that anti-tank missile somewhere! Texas Penal Code, Title 10, Chapter 46:
(2) "Explosive weapon" means any explosive or incendiary bomb, grenade, rocket, or mine, that is designed, made, or adapted for the purpose of inflicting serious bodily injury, death, or substantial property damage, or for the principal purpose of causing such a loud report as to cause undue public alarm or terror, and includes a device designed, made, or adapted for delivery or shooting an explosive weapon.
(10) "Short-barrel firearm" means a rifle with a barrel length of less than 16 inches or a shotgun with a barrel length of less than 18 inches, or any weapon made from a shotgun or rifle if, as altered, it has an overall length of less than 26 inches.
46.05. PROHIBITED WEAPONS.
(a) A person commits an offense if the person intentionally or knowingly possesses, manufactures, transports, repairs, or sells:
(1) any of the following items, unless the item is registered in the National Firearms Registration and Transfer Record maintained by the Bureau of Alcohol, Tobacco, Firearms and Explosives or otherwise not subject to that registration requirement or unless the item is classified as a curio or relic by the United States Department of Justice:
(A) an explosive weapon;
(B) a machine gun; or
(C) a short-barrel firearm;
Sec. 46.09. COMPONENTS OF EXPLOSIVES.
(a) A person commits an offense if the person knowingly possesses components of an explosive weapon with the intent to combine the components into an explosive weapon for use in a criminal endeavor.
OUCH! See that? The mounting of the missile launcher just turned the gun highly illegal, and even in the act of shortening the shotgun by altering the stock to be telescopic, it might have become illegal if the gun became too short. And it gets worse. The mere possession of the guided missile is impossible unless it's a curio or relic (which would mean it is old!) or registered, but it can't be because private citizens can't make it... and even owning the parts for the missile would be illegal if they would be used in a crime... wait, manufacturing of a missile is a crime, so owning the parts also is a crime!
Billy is screwed under both texas and federal law.