The Jagiellonian Positron Emission Tomograph (J-PET) is a novel device being developed at Jagiellonian University in Krakow, Poland based on organic scintillators. J-PET is an axially symmetric (M. Mohammed) has been affiliated to affiliation 6. Please check if correct, otherwise, provide the correct affiliation.and high acceptance scanner that can be used as a multi-purpose detector system. It is well suited to pursue tests of discrete symmetries in decays of positronium in addition to medical imaging. J-PET enables the measurement of both momenta and the polarization vectors of annihilation photons. The latter is a unique feature of the J-PET detector which allows the study of time reversal symmetry violation operator which can be constructed solely from the annihilation photons momenta before and after the scattering in the detector.