To be precise, I want to know whether the following statement is true or false:
Let $A$ be a ring (it can be reduced), $f:\rm{Spec}(A/I) \to \rm{Spec}(A)$ is a closed immersion, $\tilde{M}$ is a quasi-coherent sheaf of $\mathcal{O}_{\rm{Spec}(A)}$-module, is it true $f^{-1}(\tilde{M})$ is also a quasi-coherent sheaf of $\mathcal{O}_{\rm{Spec}(A/I)}$-module?