The paper represents Part II of a 2-part paper which provides the normal forms of piecewise linear vector fields (abbr. PL-systems) under affine conjugacy and the prototype chaotic attractors in the PL-systems. In Part I [Japan J. Appl. Math. 5, No.2, 257-304 (1988; Zbl 0672.58028)], the author has derived the general forms of continuous PL-systems with many regions and the normal forms of affine vector fields with a section, which play an important role in Part II. An affine vector field with a section is regarded as a half-part of a 2-region system and, as the author points out, the affine conjugate classes of n-dimensional 2-region systems are the most fundamental piecewise linear vector fields because the more general piecewise linear systems may be regarded as combinations of 2-region systems. In Part II the author provides the normal forms of 2-regions PL-systems and the prototype attractors (spiral, double scroll, double screw, troidal, Sparrow, Lorenz and Duffing attractors). He also proves that the affine conjugate classes of proper systems are uniquely determined by the eigenvalues in each region. The whole paper consists of 7 sections: sections 1-4 constitute Part I while Part II contains sections 5-7. After considering the normal forms of full 2-region systems in Section 5, in Section 6 the author derives the normal forms of proper 2-region piecewise linear vector fields, which are special classes of non-degenerate 2-region systems. Since the condition to be proper (i.e. invariant subspaces are not parallel to the boundary) is generic, the proper systems are important classes to study the bifurcation problem of piecewise linear vector fields. The author demonstrates that the normal forms of proper systems are determined by the values of fundamental symmetric expression of eigenvalues in each region, which are regarded as canonical bifurcation parameters. In Section 7 the author derives the normal forms of 3-dimensional 3- region systems with point symmetry, 3-dimensional 4-region systems with axial symmetry, and 4-dimensional 3-region systems with point symmetry. As it is shown, from these equations one can numerically observe various chaotic attractors depending on parameter values. Although only 3- and 4- dimensional systems are considered, the method used to derive the normal forms is valid for the general case of n-dimensional systems with many regions.