Fourier of Basis Points (Basis in Reciprocal space) (Convolution Theorem)

nyxynyx

I came across this question where there is a FCC lattice. It states that the lattice is a convolution of the simple cubic (whose reciprocal lattice is itself) with a basis (that consists of 2 points).

When finding the reciprocal of this BCC lattice,
FourierTransform(BCC)
= FourierTransform(SimpleCubic * Basis)
= FourierTransform(SimpleCubic) . FourierTransform(Basis)

Now what is the fourier transform of the basis which consists of 2 points? Thanks for any help to clear up this confusion!