  This is the second part of the work on differential models of the Anderson
duals to the stable tangential $G$-bordism theories $I\Omega^G$, motivated by
classifications of invertible QFT's. Using the model constructed in the first
part \cite{YamashitaYonekura2021}, in this paper we show that pushforwards in
generalized differential cohomology theories induces transformations between
differential cohomology theories which refine the Anderson duals to
multiplicative genera. This gives us a unified understanding of an important
class of elements in the Anderson duals with physical origins.
