Regularization of relative holonomic D-modules

Let $X$ and $S$ be complex analytic manifolds where $S$ plays the role of a parameter space. Using the sheaf ${\text{DXS}}^{\mathrm{\infty }}$ of relative differential operators of infinite order, we construct functorially the regular holonomic $\text{DXS}$-module ${\text{shm}}_{reg}$ associated to a relative holonomic $\text{DXS}$-module $\text{shm}$, extending to the relative case classical theorems by Kashiwara-Kawai: denoting by ${\text{shm}}^{\mathrm{\infty }}$ the tensor product of $\text{shm}$ by ${\text{DXS}}^{\mathrm{\infty }}$ we explicit ${\text{shm}}^{\mathrm{\infty }}$ in terms of the sheaf of holomorphic solutions of $\text{shm}$ and prove that ${\text{shm}}^{\mathrm{\infty }}$ and ${\text{shm}}_{reg}^{\mathrm{\infty }}$ are isomorphic.