We have studied the transient evolution of electrons distributed over two levels in a wide quantum well, with the two levels below the optical phonon energy, after an ultrafast interband excitation and cascade emission of optical phonons. If electrons are distributed near the top of the passive region, a temporal negative absorption appears to be dominant in the intersubband response. This is due to the effective broadening of the upper level state under the optical phonon emission. We have then considered the amplification of the ground mode in a THz waveguide with a multiquantum well placed at the center of the cavity. A huge increase of the probe signal is obtained, which permits the temporal stimulated emission regime of the photoexcited electrons in the THz spectral region.