About extension of homeomorphisms over zero-dimensional homogeneous spaces

Let $X$ be a zero-dimensional homogeneous space satisfying the first axiom of countability. We prove the theorem about an extension of a homeomorphism $g: A\to B$ to a homeomorphism $f: X\to X$, where $A$ and $B$ are countable disjoint compact subsets of the space $X$. If, additionally, $X$ is a non-pseudocompact space, then the homeomorphism $g$ is extendable to a homeomorphism $f: X\to X\setminus A$.