Reprocessing of X-ray pulsar radiation by the atmosphere of a companion in a binary system may result in reflected pulse radiation with a period of the pulses equal to the period of the pulsar under suitable conditions. In this paper the influence of the rotation of the source - the pulsar - about its axis on the parameters of thus reflected pulses is investigated. The binary system is modeled by the spherical reflective screen and the compact source uniformly rotating about its axis; the beam pattern (BP) of the source periodically runs over the surface of the screen. Irradiation of the screen by the pulses infinitely narrow in time and by the rectangular pulses is considered. In this model parameters of the pulses reflected in some directions are calculated. The main conclusion provided by the consideration of this model is that the properties of reflected pulses - their profile, and the moments of reaching the observer - substantially depend on the correlation between the light speed and the speed of the B