The answer to this has several parts. First, I am not an attorney, so consult with an attorney if you want a more licensed opinion. Second, let’s divide this question into five parts: Moral responsibility, responsibility under state law, responsibility under federal law, potential civil liability, and practical matters.

Moral responsibility. That’s easy. As a moral person and a responsible, law-abiding member of society and gun owner, we do not want to transfer a firearm (or even a car) to another person who would use it to jeopardize or injure an innocent person. We want to have some assurance that the buyer is not a criminal or dangerously careless person, and not flaky or unstable. Thus, it’s helpful in assessing character issues to be selling to someone we know well, personally.

State laws. I’m not an expert on any laws except those of my home state, so the reader will need to incorporate separately whatever his or her home state laws may require or prohibit. Montana laws do not control private transfers of firearms.

Federal laws. 18 USC § 922(d) makes it a crime to transfer a firerarm or ammunition to another person “ knowing or having reasonable cause to believe that such person” is prohibited from firearm possession, specifically:

18 USC § 922(d) says:
(d) It shall be unlawful for any person to sell or otherwise dispose of any firearm or ammunition to any person knowing or having reasonable cause to believe that such person—

(1) is under indictment for, or has been convicted in any court of, a crime punishable by imprisonment for a term exceeding one year;

(2) is a fugitive from justice;

(3) is an unlawful user of or addicted to any controlled substance (as defined in section 102 of the Controlled Substances Act (21 U.S.C. 802));

(4) has been adjudicated as a mental defective or has been committed to any mental institution;

(5) who, being an alien—

(A) is illegally or unlawfully in the United States; or
(B) except as provided in subsection (y)(2), has been admitted to the United States under a nonimmigrant visa (as that term is defined in section 101(a)(26) of the Immigration and Nationality Act (8 U.S.C. 1101(a)(26)));

(6) who has been discharged from the Armed Forces under dishonorable conditions;

(7) who, having been a citizen of the United States, has renounced his citizenship;

(8) is subject to a court order that restrains such person from harassing, stalking, or threatening an intimate partner of such person or child of such intimate partner or person, or engaging in other conduct that would place an intimate partner in reasonable fear of bodily injury to the partner or child, except that this paragraph shall only apply to a court order that—

(A) was issued after a hearing of which such person received actual notice, and at which such person had the opportunity to participate; and
(B)
(i) includes a finding that such person represents a credible threat to the physical safety of such intimate partner or child; or
(ii) by its terms explicitly prohibits the use, attempted use, or threatened use of physical force against such intimate partner or child that would reasonably be expected to cause bodily injury; or

(9) has been convicted in any court of a misdemeanor crime of domestic violence.
This subsection shall not apply with respect to the sale or disposition of a firearm or ammunition to a licensed importer, licensed manufacturer, licensed dealer, or licensed collector who pursuant to subsection (b) of section 925 of this chapter is not precluded from dealing in firearms or ammunition, or to a person who has been granted relief from disabilities pursuant to subsection (c) of section 925 of this chapter.

18 USC § 922(a)(5) makes it illegal to transfer a firearm to a person the seller knows or has reasonable cause to believe does not reside in the state of the seller. This does not include a temporary transfer such as the loan of a firearm for hunting. Here is the specific wording of the federal law:

It shall be unlawful –

(5) for any person (other than a licensed importer, licensed manufacturer, licensed dealer, or licensed collector) to transfer, sell, trade, give, transport, or deliver any firearm to any person (other than a licensed importer, licensed manufacturer, licensed dealer, or licensed collector) who the transferor knows or has reasonable cause to believe does not reside in (or if the person is a corporation or other business entity, does not maintain a place of business in) the State in which the transferor resides; except that this paragraph shall not apply to (A) the transfer, transportation, or delivery of a firearm made to carry out a bequest of a firearm to, or an acquisition by intestate succession of a firearm by, a person who is permitted to acquire or possess a firearm under the laws of the State of his residence, and (B) the loan or rental of a firearm to any person for temporary use for lawful sporting purposes

All of Section 922 is posted at https://www.law.cornell.edu/uscode/text/18/922.

Civil liability. Under the Law of Torts, the general rule is that you are not responsible for the criminal or negligent activities of another person unless you knew or should have known of their intent. That means that the default is you can assume that a buyer’s intent is lawful. However, if a seller is sued by an injured person alleging that the seller knew or should have known that the buyer would likely use the firearm sold to cause the injury, then the question will likely come before a jury to decide. In addition to having to pay an attorney to defend him, the seller could also have a stiff award against him or her and in favor of the plaintiff. Thus, a prudent seller will be cautious when selling firearms. There are ways to make the process safer.

Practical matters. When a private person (not an FFL) is selling a firearm to another private person, there are a number of ways a reasonable and prudent seller can reduce legal and moral risk.

Sell to known people. A person selling a firearm privately will be better off selling to someone the person knows well, if you have confidence that the person is not prohibited under federal law and is not a flaky or unsound person. This might be a neighbor you’ve know for years, a longtime co-worker, or a member of your gun club. Selling to unknown people is where more due diligence is required to keep the seller on safe legal and moral ground.

Other indicators. If the buyer has a currently valid concealed weapon permit, that usually means that the person has recently passed a federal background check and is not a prohibited person under federal law. If you know (for sure) that the person has recently purchased a firearm from a federally-licensed dealer, then the person has cleared the Brady Law background check system and is not a prohibited person. In either case, the prudent seller also will wish to have confidence that the buyer is a solid and stable person, and not flaky or unsound.

General impressions. A seller will want to notice other indicators to determine if a sale to a stranger is copacetic. Is the buyer driving a vehicle with license plates that match his or her claim of residence? Does any identification offered match the buyer? Is the buyer calm and businesslike or nervous and unsettled? With any red flags, it would be prudent to not consummate the sale.

Identification. Many careful people when selling a firearm privately to an unknown buyer will ask the buyer to present identification such as a drivers license, and will write down relevant information from the ID.

Receipt and records. A private seller should also prepare a duplicate receipt for the sale that includes the name and ID type and number of the buyer. It should also include the date of the sale, and the make, model and serial number of the firearm. The buyer should want a copy of this receipt in case the buyer is ever asked to prove that he or she obtained the firearm lawfully. The seller should definitely retain a copy of the receipt. If some law enforcement agent ever comes to the seller claiming that the sold firearm has been retrieved from a crime scene, it will be ever so helpful to have this receipt to document the transfer out of the seller’s possession.

Finally. If all usual vetting fails to get a seller into a comfort zone about a particular buyer, yet the seller really wants to make the sale, the seller can always ask the buyer to meet him at the location of a willing licensed firearms dealer (”FFL”), such as a gunsmith or pawn shop that handles guns, where the buyer can be run through a Brady Law check for the sale. Phone the FFL in advance to confirm availability of and price for this service, which may range from $25 to $60. If the buyer refuses do a transfer via an FFL, then the buyer may be a person the seller doesn’t wish to sell a firearm to. Remember, it’s willing seller, willing buyer.

Depending on your state laws and compliance with these laws and principles, it is perfectly legal and possible for private individuals to sell firearms to other individuals.