  This is the second part of the paper devoted to the general proof of
canonicity of Baecklund transformation (BT) for a Hamiltonian integrable system
governed by SL(2)-invariant r-matrix. Introducing an extended phase space from
which the original one is obtained by imposing a 1st kind constraint, we are
able to prove the canonicity of BT in a new way. The new proof allows to
explain naturally the fact why the gauge transformation matrix M associated to
the BT has the same structure as the Lax operator L. The technique is
illustrated on the example of the DST chain.
