My question is an attempt to understand the proof of lemma 6.17.3 (page 164) in the Stacks Project: http://www.math.columbia.edu/algebraic_geometry/stacks-git/book.pdf
This lemma states:
Let $F$ be a presheaf of sets on $X$. Any map $F\to G$ into a sheaf of sets factors uniquely as $F \to F^{S} \to G$ (when $F^{S}$ denotes the sheafification of $F$).
The part that I'd like to understand is: why is the above map $F^{S} \to G$ unique?