False.Without background checks, it is perfectly legal for anyone other than a licensed dealer to sell a gun to any of the people listed.
It is illegal to sell a gun to anyone you have reason to believe cannot legally own a gun.
So, since you know your know you mom is a felon, selling her a gun breaks the law.
There is no requirement to know or to even find out who you sell a gun to unless it is one of the regulated types. If they are willing to pay your price, you can sell them a gun. Not even a sales receipt required.
IF the ATF come to your door and want to know where the gun is because it was used in a crime, YOU BETTER KNOW WHO YOU SOLD IT TO!!
It is called "tracing a gun used in a crime".
It might be a good idea to know who you sold your gun to, and whether or not they can legally possess/own a firearm.