Abstract The explicit expressions for linearly optical conductivity and absorption power of electromagnetic wave caused by confined electrons in the hyperbolic quantum well is obtained in the case of electron-longitudinal optical phonon scattering. Linearly optically detected electrophonon resonance (ODEPR) effect in a specific GaAs/AlAs hyperbolic quantum well with P¨oschl-Teller potential type is investigated. Conditions for ODEPR are discussed based on the curves expressing the dependence of absorption power on the photon energy. From these curves we obtained ODEPR - linewidths as profiles of the curves. Computational results show that linear ODEPR- linewidths increase with temperature and decrease with well parameters. Keywords absorption power, quantum well, hyperbolic, P¨oschl Teller potential, ODEPR- linewidths