  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 middle paper, we adapt a method used by Shelah in
\cite{ShelahPermutation} and \cite{ShelahPermutationErrata}, and by Shelah and
Truss in \cite{ShelahTrussQuotients} to define a cone transitive CFPO inside
its automorphism group using the language of group theory.
