Generalization of order separability for free products and omnipotence of free products of groups

It was proved that for any finite set of elements of a free product of residually finite groups such that no two of them belong to conjugate cyclic subgroups and each of them do not belong to a subgroup which is conjugate a to free factor there exists a homomorphism of the free product onto a finite group such that the order of the image of each fixed element is an arbitrary multiple of a constant number.