Let $(R, \mathfrak{m}) $ be a local $k$- algebra and $\Omega^{1}_{R}$ denote the module of Kahler differential. Does the canonical map $ \Omega^{1}_{R} \otimes_{R} \hat{R} \rightarrow \Omega^{1}_{\hat{R}}$ is an isomorphism?, where $\hat{R}$ is the completion of $R$ with respect to $\mathfrak{m}$ and $k$ is any field of characteristics $0$.

If not, under what condition on $R$ turn this map to be isomorphism?. Is smoothness of $R$ will suffices to conclude this?