  Part I proved that for every quasivariety K of structures (which may have
both operations and relations) there is a semilattice S with operators such
that he lattice of quasi-equational theories of K (the dual of the lattice of
sub-quasivarieties of K) is isomorphic to Con(S,+,0,F). It is known that if S
is a join semilattice with 0 (and no operators), then there is a quasivariety Q
such that the lattice of theories of Q is isomorphic to Con(S,+,0). We prove
that if S is a semilattice having both 0 and 1 with a group G of operators
acting on S, and each operator in G fixes both 0 and 1, then there is a
quasivariety W such that the lattice of quasi-equational theories of W is
isomorphic to Con(S,+,0,G).
