  In this triple of papers, we examine when two cycle-free partial orders can
share an abstract automorphism group. This question was posed by M. Rubin in
his memoir concerning the reconstruction of trees.
  In this final paper, we give describe a way of constructing `decorated' CFPOs
by attaching treelike CFPOs to and between the elements of a cone transitive
CFPO. We then show that the automorphism groups of the components of of a
decorated CFPO are second order definable in the abstract automorphism group of
the decorated CFPO.
