  We present a derivation of the last unknown part of the $\alpha^7m$
contribution to the Lamb shift of a two-electron atom, induced by the radiative
QED effects beyond the Bethe logarithm. This derivation is performed in the
framework of nonrelativistic quantum electrodynamics and is valid for the
triplet (spin $S = 1$) atomic states. The obtained formulas are free from any
divergences and are suitable for a numerical evaluation. This opens a way for a
complete numerical calculation of the $\alpha^7m$ QED effects in helium, which
will allow an accurate determination of the nuclear charge radius from
measurements of helium transition frequencies.
