  Parabolic almost conformally symplectic structures were introduced in the
first part of this series of articles as a class of geometric structures which
have an underlying almost conformally symplectic structure. If this underlying
structure is conformally symplectic, then one obtains a PCS-structure. In the
current article, we relate PCS-structures to parabolic contact structures.
Starting from a parabolic contact structure with a transversal infinitesimal
automorphism, we first construct a natural PCS-structure on any leaf space of
the corresponding foliation. Then we develop a parabolic version of
contactification to show that any PCS-structure can be locally realized
(uniquely up to isomorphism) in this way.
  In the second part of the paper, these results are extended to an analogous
correspondence between contact projective structures and so-called conformally
Fedosov structures. The developments in this article provide the technical
background for a construction of sequences and complexes of differential
operators which are naturally associated to PCS-structures by pushing down BGG
sequences on parabolic contact structures. This is the topic of the third part
of this series of articles.
