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The behavior of levels near the threshold of the lower continuum insuperheavy H-like atoms with $Z\alpha >1$, caused by the interaction $\DeltaU_{AMM}$ of the electron's magnetic anomaly (AMM) dynamically screened at smalldistances $ \ll 1/m$, with the Coulomb field of atomic nucleus is considered bytaking into account the complete dependence of electron's wavefunction (WF) on$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, consideredas a uniformly charged extended Coulomb source, leads to results, whichcoincide within the accepted precision of calculations. It is shown also thatthere appears some difference in results between perturbative andnon-perturbative methods of accounting for the contribution from $\DeltaU_{AMM}$ within the corresponding Dirac equation (DE) in favor of the latter.Moreover, the growth rate of the contribution from $\Delta U_{AMM}$ reaches itsmaximum at $ Z \sim 140-150$, while by further increase of $Z$ into thesupercritical region $Z\gg Z_{cr,1}$ the shift of levels caused by $\DeltaU_{AMM}$ near the lower continuum decreases monotonically to zero. The lastresult is generalized to the whole self-energy contribution to the shift oflevels and so to the possible behavior of radiative QED-effects with virtualphoton exchange near the lower continuum.

Perturbativity vs non-perturbativity in QED-effects for H-like atoms with $Z\alpha >1$