  This is the second of two papers dedicated to the computation of the reduced
C*-algebra of a connected, linear, real reductive group up to C*-algebraic
Morita equivalence, and the verification of the Connes-Kasparov conjecture for
these groups. These results were originally announced by Antony Wassermann in
1987. In Part I we presented the Morita equivalence and the Connes-Kasparov
morphism. In this part we shall compute the morphism using David Vogan's
description of the tempered dual.
