  In this paper we continue our derivation of the correlation functions of open
quantum spin 1/2 chains with unparallel magnetic fields on the edges; this time
for the more involved case of the XXZ spin 1/2 chains. We develop our study in
the framework of the quantum Separation of Variables (SoV), which gives us both
the complete spectrum characterization and simple scalar product formulae for
separate states, including transfer matrix eigenstates. Here, we leave the
boundary magnetic field in the first site of the chain completely arbitrary,
and we fix the boundary field in the last site $N$ of the chain to be a
specific value along the $z$-direction. This is a natural first choice for the
unparallel boundary magnetic fields. We prove that under these special boundary
conditions, on the one side, we have a simple enough complete spectrum
description in terms of homogeneous Baxter like $TQ$-equation. On the other
side, we prove a simple enough description of the action of a basis of local
operators on transfer matrix eigenstates as linear combinations of separate
states. Thanks to these results, we achieve our main goal to derive correlation
functions for a set of local operators both for the finite and half-infinite
chains, with multiple integral formulae in this last case.
