Does it induce a $\mathcal F^{\dagger}$-module $\mathcal M^{\dagger}$?

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Let $\mathcal F$ be a presheaf of rings on topological space $X$, and let $\mathcal M$ be a presheaf of $\mathcal F$-modules. Does it induce a $\mathcal F^{\dagger}$-module $\mathcal M^{\dagger}$?