Esakia's theorem for the amended monadic intuitionistic calculus

We show that the amended monadic Grzegorczyk logic ${\mathsf{M}}^{+}\mathsf{G}\mathsf{r}\mathsf{z}$ is the largest modal companion of the amended monadic intuitionistic logic ${\mathsf{M}}^{+}\mathsf{I}\mathsf{P}\mathsf{C}$. Thus, unlike the monadic intuitionistic logic $\mathsf{M}\mathsf{I}\mathsf{P}\mathsf{C}$, Esakia’s theorem does extend to ${\mathsf{M}}^{+}\mathsf{I}\mathsf{P}\mathsf{C}$.