Injective module sheaves are flasque

For opens $U\subseteq V\subseteq X$, there is a monomorphism between the extensions by zero of ${\mathcal{O}}_U$ and ${\mathcal{O}}_V$. Morphisms from these sheaves into an injective sheaf of modules $I$ identify with sections on $U$ and $V$, respectively. The injective object extension property therefore makes the restriction $I(V)\to I(U)$ surjective, proving that $I$ is flasque. The argument applies to any ringed space.