  The electron shell of the daughter atoms often appears excited in the
double-$\beta$ decays, which causes a change in the energy taken away by
$\beta$-electrons. The average value and variance of the excitation energy of
the electron shell of the daughter atom are calculated for the double-$\beta$
decay of germanium $_{32}^{76}\mathrm{Ge} \rightarrow
_{34}^{76}\mathrm{Se}^*+2\beta^-(+~2\bar{\nu_e})$ in both the Thomas--Fermi
model and the relativistic Dirac--Hartree--Fock theory. Using the results
obtained, a two-parameter model of the energy spectrum of $\beta$-electrons in
the neutrinoless mode is constructed, taking into account reaction energy
redistribution in the decay channels. The shift in total energy of
$\beta$-electrons is found to be under 50 eV at a confidence level of 90%. The
average excitation energy, on the other hand, is an order of magnitude higher
and equal to $\sim 400$ eV, while the square root of the variance is equal to
$\sim 2900$ eV, which is presumably explained by the contribution of the core
electrons to the energy characteristics of the process. The probability is
nearly saturated with excitations with a small amount of released energy, which
is common for the outermost electrons. The distortion of the peak shape of the
neutrinoless double-$\beta$ decay should be taken into consideration when
analyzing data from detectors with a resolution of $\sim 100$ eV or higher.
