By utilizing homomorphisms and -strong semilattice of semigroups, we show that the Green (_*,~)-relation H^*,~ is a regular band congruence on a r-ample semigroup if and only if it is a G-strong semilattice of completely J^*,~-simple semigroups. The result generalizes Petrich’s result on completely regular semigroups with Green’s relation H a normal band congruence or a regular band congruence from the round of regular semigroups to the round of r-ample semigroups.