We have applied conventional Time Differential Perturbed Angular Correlation (TDPAC) method to observe the anisotropy oscillations in the 3 gamma annihilation decay of polarized Positronium in a weak magnetic field. The effect, as predicted theoretically and experimentally demonstrated by Barishevsky et al. [V. G. Barishevsky, O.N. Metelitsa, V. V. Tikhomirov, Oscillations of the positronium decay gamma-quantum angular distribution in a magnetic field, J. Phys. B: At. Mol. Opt. Phys. 22 (1989) 2835], is induced by the coherent admixture of the m = 0 states of ortho-Positronium (o-Ps) and para-Positronium (p-Ps) in interaction with the magnetic field. The following experimental characteristics are to be considered: (i) the oscillation frequency corresponds to the difference in energy of the Ps atom levels in magnetic field and is proportional with H-2; (ii) in a fixed geometry the modulation depth (oscillations amplitude) depends on the mean positron polarization; (iii) privileged angles of the polarization vector, magnetic field and detectors are required for optimizing the observed oscillations amplitude. The normalized difference spectrum function (R(t)) obtained from time spectra measured in vacuum and in different gaseous atmospheres (Ar, H-2, N-2) have the oscillations amplitude constant and we conclude that the Ps atoms are not fully thermalized over a time interval of about 400 ns. The R(t) functions obtained for o-Ps annihilation decays, in dry air or Ar-O mixture, have the oscillations amplitude time dependent due, probably, to the paramagnetism of the Oxygen molecules. (C) 2008 Elsevier B.V. All rights reserved.