  The behavior of levels near the threshold of the lower continuum in
superheavy H-like atoms with $Z\alpha >1$, caused by the interaction $\Delta
U_{AMM}$ of the electron's magnetic anomaly (AMM) dynamically screened at small
distances $ \ll 1/m$, with the Coulomb field of atomic nucleus is considered by
taking into account the complete dependence of electron's wavefunction (WF) on
$Z\alpha$. It is shown that the calculation of the contribution caused by
$\Delta U_{AMM}$ via both the quark structure and the whole nucleus, considered
as a uniformly charged extended Coulomb source, leads to results, which
coincide within the accepted precision of calculations. It is shown also that
there appears some difference in results between perturbative and
non-perturbative methods of accounting for the contribution from $\Delta
U_{AMM}$ within the corresponding Dirac equation (DE) in favor of the latter.
Moreover, the growth rate of the contribution from $\Delta U_{AMM}$ reaches its
maximum at $ Z \sim 140-150$, while by further increase of $Z$ into the
supercritical region $Z\gg Z_{cr,1}$ the shift of levels caused by $\Delta
U_{AMM}$ near the lower continuum decreases monotonically to zero. The last
result is generalized to the whole self-energy contribution to the shift of
levels and so to the possible behavior of radiative QED-effects with virtual
photon exchange near the lower continuum.
