I have proved the following negative result:
Theorem is not boolean if is a non-atomic boolean lattice.
The theorem is presented in this file.
denotes the set of pointfree funcoids from a poset to a poset (see my free ebook).
The theorem and its proof were modeled after theorem 3.8 in this article (December 1979) by Zahava Shmuely.
It would be probably interesting to a find a common generalization of my theorem and the original Zahava Shmuely’s one.