Let $X$ be a Hausdorff locally compact topological space, $R$ be a sheaf of $\mathbb{C}_X$-algebras on $X$. If necessary, we can assume that $(X,R)$ is a complex manifold. If $M$ is an injective object of the category $\mathrm{Mod}(R)$, and $x\in X$, then is the stalk $M(x)$ an injective $R(x)$-module?
It is proved in 6.24, p.448 of "Analytic $D$-modules and applications" by Björk. But I cannot understand his proof at all.
Below, for a sheaf $F$ on $X$ and a closed embedding $j:Z\to X$, the sheaf $j_*j^{-1}F$ is denoted by $F_Z$. The collection of injective $R$-modules is denoted by $i(R)$.
