If the FFL is transferring the firearm to an individual (either the person buying your gun or you if the transfer is for your gun), then a ATF Form 4473 and NICS background check (with some exceptions) must be completed.
Texas law says that a person cannot give or sell a firearm to a child younger than 18 years of age. The state law about illegal transfers or sales of weapons is in Section 46.06 of the Texas Penal Code.
Notarization of the Firearm Bill of Sale is not mandatory in Texas. However, this step will protect you in case of a conflict or dispute.
It's perfectly fine receiving a firearm as a gift as long as YOU as an individual don't fall under a prohibited person that cannot possess a firearm.
Many gun owners in Texas ask, “How do I register my gun?” In Texas, a gun buyer or seller does not have to go through a registration process for firearms. And the state does not register firearms to an owner. Other states, such as Illinois or New Jersey, require gun owners to register with the state.
Cons: Regulatory Requirements: Obtaining and maintaining an FFL involves complying with a significant number of federal regulations. Failure to adhere to these regulations can result in the revocation of the license and legal consequences.
Firearm Prohibitions in Texas Under federal law, people are generally prohibited from purchasing or possessing firearms if they have been convicted of a felony or some domestic violence misdemeanors, or if they are subject to certain court orders related to domestic violence or a serious mental condition.
Registration Laws The State of Texas does not maintain a registry of firearms. The federal government also does not maintain a general registry of handgun or rifle ownership.