Why do BF3 and NH3 react when B has an expanded octet in the adduct?

I know that some elements like sulfur are able to have an expanded octet due to vacant $\mathrm{d}$ orbitals. However, boron and nitrogen do not have any such vacant place so how is it that $\ce{NH3}$ with its extra electron pair is able to share it with $\ce{BF3}$ and form a compound?


This is an example of a Lewis acid-base reaction that I read in my textbook.


