Characterization of the pull-back of \({\mathcal D}\)-modules (Q1974552)

Let \(f: X\to Y\) be a smooth morphism of smooth algebraic varieties \(X\) and \(Y\) over \(\mathbb C.\) If a coherent \(\mathcal D_X\)-module \(\mathcal M\) is the pull-back of a coherent \(\mathcal D_Y\)-module, the characteristic variety \(\text{Ch}({\mathcal M})\) of \({\mathcal M}\) satisfies \[ \text{Ch}(\mathcal M)\subset X\times_YT^\ast Y. \tag{1} \] Conversely let \(\mathcal M\) be an algebraic \(\mathcal D_X\)-module such that (1) holds. It is a natural question to ask when such an \(\mathcal M\) is the pull-back of a \(\mathcal D_Y\)-module. The author proves that the condition (1) implies that \(\mathcal M\) is always the pull-back of a coherent \(\mathcal D_Y\)-module globally on \(X\) if \(f\) is a proper smooth morphism with simply connected fiber.