The ring homomorphism between a commutative ring $R$ and its localization $S^{-1}R$ is invertible on $S$

Question

Let $R$ be a commutative ring, and $S$ be a multiplicative subset, let $S^{-1}R$ be the localization, and defines a ring homomorphism $l: R\to S^{-1}R$ such that $l(a)=\frac{a}{1}$. Can someone tell me or give me some hints on why $l(s)$ is invertible for every $s\in S$? Thank you!