The formalism derived for the boson-fermion and the baryon mapping in Part I of
this series is applied to the single-orbit quark shell model developed by Petry
and coworkers for the description of nuclear properties. The multiquark space
is reduced to the collective subspace of multinucleon states. A collective
representation of states and operators in terms of bosons and ideal fermions or
in terms of ideal baryons, respectively, is constructed. The results of the
original model in the multinucleon space are exactly reproduced. Finally, the
two transformations are compared with  a related mapping technique recently
published by Pittel, Engel, Dukelsky, and Ring.