I'm reading Lei Fu's "Etale Cohomology Theory".
Proposition 3.2.7. Let $(S,\gamma)$ be a pointed connected noetherian scheme, $X_1$ and $X_2$ two etale covering spaces of $S$, $u: X_1\to X_2$ an $S$-morphism, and $X_i(\gamma)(i=1,2)$ the sets of geometric points of $X_i$ lying above $\gamma$. If the map $X_1(\gamma)\to X_2(\gamma)$ induced by $u$ is bijective, then $u$ is an isomorphism.
We denote $X_2\to S$ by $g_2$. Let $s\in S$ be the image of $\gamma$ and let $x_2\in X_2$ be a point above $s$. Why is there one and only one $f\in X_2(\gamma)$ such that $g_2f=\gamma$ and the image of $f$ is $x_2$?