Congruence-simple acts over completely simple semigroups

We prove that an act $X$ over a completely simple semigroup $S=\mathcal M (G,I,\Lambda,P)$ is congruence-simple (i.e., it has no nontrivial congruences) if and only if one of the following conditions holds: (1) $|X|=1$; (2) $|X|=2$ and $|XS|=1$; (3) $X=\{z_1,z_2\}$, where $z_1$ and $z_2$ are zeros; (4) $X\cong R/\rho$, where $R$ is a minimal right ideal of the semigroup $S$ and $\rho$ is a maximal proper congruence of the right ideal $R$, which is considered as an act over $S$. We describe these congruences.