  This is the continuation of the article \cite{Z23}. In this article we will
give a detailed analysis of the quantum difference equation of the equivariant
$K$-theory of the affine type $A$ quiver varieties. We will give a good
representation of the quantum difference operator $\mathbf{M}_{\mathcal{L}}(z)$
such that the monodromy operator $\mathbf{B}_{\mathbf{m}}(z)$in the formula can
be written in the $U_{q}(\mathfrak{sl}_2)$-form or in the
$U_{q}(\hat{\mathfrak{gl}}_1)$-form. We also give the detailed analysis of the
connection matrix for the quantum difference equation in the nodal limit
$p\rightarrow0$. Using these two results, we prove that the degeneration limit
of the quantum difference equation is the Dubrovin connection for the quantum
cohomology of the affine type $A$ quiver varieties, and the monodromy
representation for the Dubrovin connection is generated by the monodromy
operators $\mathbf{B}_{\mathbf{m}}$.
