We present a theory of photoluminescence in the presence of a quantizing magnetic field for a quasi-two-dimensional electron gas interacting with the lattice assuming a weak Fröhlich interaction with bulk longitudinal optical (LO) phonons. Unlike in the conventional cyclotron resonance, the calculated photoluminescence spectrum for high electron concentrations exhibits strong renormalization due to the resonant electron-phonon coupling between two quasiholes in conduction Landau levels whenever the LO-phonon energy is close to the energy difference between any two occupied Landau levels. The high electron concentration is necessary to push the Fermi energy well above that of LO phonons. The screening of the electron-phonon interaction was included within the static random-phase approximation and the finite extent of the electron wave function in the quantum well was accounted for. The calculated spectra are in excellent agreement with experimental photoluminescence data for GaAs/InxGa1-xAs/AlyGa1-yAs quantum wells.