  This is the second part of a paper describing a new concept of separation of
variables applied to the classical Clebsch integrable case. The quadratures
obtained in Part I (also uploaded in arXiv.org) lead to a new type of the Abel
map which contains Abelian integrals on two different algebraic curves.
  Here we interprete it as from the product of the two curves to the Prym
variety of one of them, show that the map is well defined although not a
bijection. We analyse its properties and formulate a new extention of the
Riemann vanishing theorem, which allows to invert the map in terms of
theta-functions of higher order.
  Lastly, we describe how to express the original variables of the Clebsch
system in terms of the preimages of the map. This enables one to obtain
theta-function solution whose structure is different from that found long time
ago by F. K\"otter.
