The absorption band shape of the combined optical quantum transition with the creation of a two-dimensional magnetoexciton and with the simultaneous excitation of one back- ground electron between its Landau levels is discussed. The combined magnetoexciton- cyclotron resonance (MECR) quantum transitions are described within the frame of the model of two-dimensional electron-hole system in a strong perpendicular magnetic field, taking into account supplementary small concentration of background electrons resident on the lowest Landau level (LLL). The concrete case of magnetoexciton composed by electron and hole on their LLL and the accompanying cyclotron resonance with excitation of the background electron from the LLL to the first excited Landau level is considered. The position of the combined absorption band is shifted in comparison with the frequency of the magnetoexciton band by the frequency of the electron cyclotron resonance. The maximal band width equals the ionization potential l I of the magnetoexciton, because participation of the third particle side by side with the electron-hole pair permits to uncover its entire internal energy spectrum beginning with the bottom of the magnetoexciton band and finishing with its ionization potential. The analytical formulas describing the absorption band shape in the vicinity of these two limiting frequencies were deduced. The numerical calculations on the base of a general formula permitted us to obtain a full band shape, which has a monotonic decreasing form with a maximal value near the frequency corresponding to the bottom of the magnetoexciton band and tends linearly to zero near the second limiting frequency corresponding to the ionization of magnetoexciton. This band shape is completely different from the case of the combined exciton-cyclotron resonance quantum transitions with participation of the two-dimensional Wannier-Mott exciton in quantum well structures revealed and discussed in references [1, 2].