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

A new approach to separation of variables for the Clebsch integrable system. Part II: Inversion of the Abel--Prym map