Cantor property of quasi-unitary acts over completely (0-)simple semigroups

A universal algebra $A$ is called cantorian if for any algebra $B$ of the same signature, the existence of injective homomorphisms $A\to B$ and $B \to A$ implies an isomorphism of algebras $A$ and $B$. A right act $X$ over a semigroup $S$ is called quasiunitary if $X=XS$. We prove that every quasiunitary act over a completely simple semigroup and also every quasiunitary act with zero over a completely 0-simple semigroup are cantorian.