Let $X,Y$ and $Z$ be stacks over $\operatorname{Sch}/\operatorname{Spec}k$ and suppose that vertical arrow $X \times_Z Y \to X$ of the diagram $\require{AMScd}$ \begin{CD} X \times_Z Y @>{}>> Y\\ @VVV @VVV\\ X @>{}>> Z \end{CD} is a representable morphism of stacks.
Is the morphism $Y \to Z$, then a representable morphism of stacks?