So if Mr. Smith is a convicted felon, you think you can "gift" him a firearm? It is indeed relevant.
If you give your father the money to go buy the gun for you because you are too young to purchase it, or otherwise not qualified, it is a straw purchase, and illegal for you and him.
As stated above, the legality of the final recipient of the firearm to possess firearms is COMPLETELY IRRELEVENT to the concept of straw purchases.
Straw purchases is buying a gun on behalf of someone else period. Straw purchase stops there. Straw purchase usually involves receiving some compensation for either the gun itself or for the act of buying the gun.
Furnishing a firearm to an ineligible person, either as a gift or as a sale is a completely seperate issue from Straw purchase.
A straw purchase and furnishing a firearm to an ineligible person can occur during the same act, or can occur as seperate acts, or each act can occur singly without the other act being committed at all.
Buying the gun for the son, with the son's money, is straw purchase.
Giving a gift of a gun to the son, who is ineligible to POSSESS that gun (notice, not purchase, but possess), is furnishing a firearm to an inelligible person.
Buying the gun for the son, with the son's money, and the son is also ineligible to POSSESS that gun, is BOTH a straw purchase AND furnishing a firearm to an inelligible person.
Any other person, obviously, may be subsitituted for the son in these cases.