Inverse of Heyting algebra morphism is p-morphism

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It is known that the category of Heyting algebras is dually equivalent to the category of Esakia spaces (which is equivalent to the category of descriptive intuitionistic Kripke frames). Under the duality, a Heyting morphism $f : H \to H'$ is send to its inverse, that is it sends a prime filter in $H'$ to its inverse image.

Question: Why is this inverse map a p-morphism (or bounded morphism)?

All references I have found for this refer to a paper by Esakia himself, in Russian. I am looking for an English reference or a proof.