Irreducible in $S^{-1}R$ implies numerator irreducible in R?

Question

I would like to prove the following;

Let $R$ be UFD and $S \subset R$, $S$ is multiplicative, $1_R \in S$.

Claim: If $r/s$ is irreducible in $S^{-1}R$ then there exists $r'/s'$ s.t $r/s\sim r'/s'$ and $r'$ is irreducible in R.

I feel like it should be true, but simply playing with elements has gotten me nowhere.