FFL is just being stupid.
The gift 'instructions' are right on the back of the 4473. and this would be a gift if you gave her the gun.
A 'straw purchase' is lying on question 11 a) on the front of the 4473.
It does not involve a prohibited person.
Even gifting a gun to a prohibited person is illegal, but would still not be a straw purchase unless they gave you the money for the gun (before or after you purchased it.
It is astounding how many folks seem to sign the form without actually READING it (and that includes the instructions).
I have a bridge for sale for you all.