  In this paper we consider the re-processing of high frequency photons emitted
by HeII and HeI during the epoch of cosmological recombination by HeI and HI.
We demonstrate that, in comparison to computations which neglect all feedback
processes, the number of cosmological recombination photons that are related to
the presence of helium in the early Universe could be increased by ~40%-70%.
Our computations imply that per helium nucleus ~3-6 additional photons could be
produced. Therefore, a total of ~12-14 helium-related photons are emitted
during cosmological recombination. This is an important addition to
cosmological recombination spectrum which in the future may render it slightly
easier to determine the primordial abundance of helium using differential
measurements of the CMB energy spectrum. Also, since these photons are the only
witnesses of the feedback process at high redshift, observing them in principle
offers a way to check our understanding of the recombination physics. Here most
interestingly, the feedback of HeII photons on HeI leads to the appearance of
several additional, rather narrow spectral features in the HeI recombination
spectrum at low frequencies. Consequently, the signatures of helium-related
features in the CMB spectral distortion due to cosmological recombination at
some given frequency can exceed the average level of ~17% several times. We
find that in particular the bands around nu ~10GHz, ~35GHz, ~80GHz, and ~200GHz
seem to be affected strongly. In addition, we computed the changes in the
cosmological ionization history, finding that only the feedback of primary HeI
photons on the dynamics of HeII-->HeI recombination has an effect, producing a
change of DN_e/N_e ~+ 0.17% at z~2300. This result seems to be ~2-3 times
smaller than the one obtained in earlier computations for this process
(abridged).
