  We study the non-conservation of the chiral charge of Dirac fields between
past and future null infinity due to the Adler-Bell-Jackiw chiral anomaly. In
previous investigations \cite{dR21}, we found that this charge fails to be
conserved if electromagnetic sources in the bulk emit circularly polarized
radiation. In this article, we unravel yet another contribution coming from the
non-zero, infrared "soft" charges of the external, electromagnetic field. This
new contribution can be interpreted as another manifestation of the ordinary
memory effect produced by transitions between different infrared sectors of
Maxwell theory, but now on test quantum fields rather than on test classical
particles. In other words, a flux of electromagnetic waves can leave a memory
on quantum fermion states in the form of a permanent, net helicity. We
elaborate this idea in both $1+1$ and $3+1$ dimensions. We also show that, in
sharp contrast, gravitational infrared charges do not contribute to the fermion
chiral anomaly.
