commutative algebra – Is $widehat{IM}=widehat I widehat M? $ for any finitely generated module $M$ , where $widehat {(-)}$ denotes completion w.r.t. maximal ideal?

Let $(R,mathfrak m)$ be a Noetherian local ring, and let $(widehat R, widehat{mathfrak m})$ be its $mathfrak m$-afic completion. Let $M$ be a finitely generated $R$-module.

Then, is it true that $widehat{IM}=widehat I widehat M? $

I know this is true if $I=mathfrak m$ as explained here If $M$ be a finitely generated module over a Noetherian ring $A,$ then $widehat{aM}=hat{a} hat{M}.$ , but I’m not sure what happens for general $I$. Please help.