When is the pushforward of a sheaf isomorphic to the pullback along a section?

Question

Let $p:X\to S$ be a morphism of schemes, and let $\mathcal{F}$ be a $\mathcal{O}_X$-module on $X$. Suppose $s:S\to X$ is a section of $p$. Then when do we have an isomorphism $s^{\ast}\mathcal{F}\cong p_{\ast}\mathcal{F}$?