  This article reports on the feasibility of testing of the symmetry under
reversal in time in a purely leptonic system constituted by positronium atoms
using the J-PET detector. The present state of T symmetry tests is discussed
with an emphasis on the scarcely explored sector of leptonic systems. Two
possible strategies of searching for manifestations of T violation in
non-vanishing angular correlations of final state observables in the decays of
metastable triplet states of positronium available with J-PET are proposed and
discussed. Results of a pilot measurement with J-PET and assessment of its
performance in reconstruction of three-photon decays are shown along with an
analysis of its impact on the sensitivity of the detector for the determination
of T -violation sensitive observables.
