The magnetic-field dependence of the operation of a quantum-cascade intersubband laser (QCL) is used to investigate the energetic relaxation of injected electrons through phonon emission. The QCL emits at 3.8 mu m and incorporates a strain-compensated active region with a large degree of internal strain. Energies of the relevant electron-phonon scattering responsible for the depopulation of the upper laser level are determined from the analysis of the Landau-level spectra. A comparison of those energies with the Raman spectrum of the active region is used to identify which phonon is primarily involved in the electron-phonon scattering. In spite of the low Ga-content in the (In,Ga)As quantum wells and high Al-content in the AlAs/(In,Al)As composite barriers, the depopulation of the upper laser level appears to be dominated by the resonant electron-GaAs-like-longitudinal-phonon intersubband scattering. In particular, the contribution due to AlAs-like modes is negligible. (C) 2005 American Institute of Physics.