  We discuss the analytic aspects of the geometric model for $K$-homology with
coefficients in $\mathbb{Z}/k\mathbb{Z}$ constructed in "Geometric K-homology
with coefficients I". In particular, using results of Rosenberg and Schochet,
we construct a map from this geometric model to its analytic counterpart.
Moreover, we show that this map is an isomorphism in the case of a finite
CW-complex. The relationship between this map and the Freed-Melrose index
theorem is also discussed. Many of these results are analogous to those of Baum
and Douglas in the case of $spin^c$ manifolds, geometric K-homology, and
Atiyah-Singer index theorem.
