  In the prequel of this paper, we have associated a family of cluster
X-varieties to the dual Poisson-Lie group(G*,\pi_*) of (G,\pi_G) when (G,\pi_G)
is a complex semi-simple Lie group of adjoint type, given with the standard
Poisson structure \pi_G and \pi_* is the "dual" Poisson structure defined by
the Semenov-Tian-Shansky Poisson bracket on G. We describe here the cluster
combinatorics involved into the Artin group action on G* given by the
De-Concini-Kac-Procesi Poisson automorphisms.
