  Calculating the (a,c) ring of the maximal phase orbifold for `invertible'
Landau--Ginzburg models, we show that the Berglund--H"ubsch construction works
for all potentials of the relevant type. The map that sends a monomial in the
original model to a twisted state in the orbifold representation of the mirror
is constructed explicitly. Via this map, the OP selection rules of the chiral
ring exactly correspond to the twist selection rules for the orbifold. This
shows that we indeed arrive at the correct point in moduli space, and that the
mirror map can be extended to arbitrary orbifolds, including non-abelian twists
and discrete torsion, by modding out the appropriate quantum symmetries.
