Strong increase in the intensity of the peaks of excited magneto-exciton (ME) states in the photoluminescence excitation (PLE) spectra recorded for the ground heavy-hole magneto-excitons (of the 1sHH type) has been found in a GaAs/AlGaAs superlattice in strong magnetic field B applied normal to the sample layers. While varying B the intensities of the PLE peaks have been measured as functions of energy separation $Delta E$ between excited ME peaks and the ground state of the system. The resonance profiles have been found to have maxima at $Delta E_{rm max}$ close to the energy of the GaAs LO-phonon. However, the value of $Delta E_{rm max}$ depends on quantum numbers of the excited ME state. The revealed very low quantum efficiency of the investigated sample allows us to ascribe the observed resonance to the enhancement of the non-radiative magneto-exciton relaxation rate arising due to LO-phonon emission. The presented theoretical model, being in a good agreement with experimental observations, provides a method to extract 1sHH magneto-exciton ``in-plane dispersion from the dependence of $Delta E_{rm max}$ on the excited ME state quantum numbers.
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