We have investigated the nature and the stability of the high T c (∼ 8 K) and low T c (∼ 1.5 K) superconducting phases (respectively called β-H and β-L) of the organic conductor β-(BEDT-TTF) 2I 3, using different and complementary techniques. First, by resistivity measurements and following a well-defined temperature-pressure cycling process (namely the release of the high pressure at low temperature), we show that the β-H phase is stabilized at ambient pressure and low temperature, exhibiting a very sharp and complete superconducting transition at 8.1 K and 1 bar. Secondly, an AC-susceptibility study reveals that this state is stable and exhibits bulk superconductivity at high T c and ambient P as long as the sample is not warmed above 125 K. Finally, we present NMR results on the 1H spin-lattice relaxation rate behaviour in both the β-H phase (under pressure and at 1 bar) and the β-L phase. A very clear field-dependent anomaly is observed at the superconducting transition and is attributed to a logarithmic critical singularity whose amplitude is enhanced by the low dimensional character of this conductor. In conclusion, we shall discuss the nature of the β-H and β-L phases with respect to the crystallographic transitions reported at 1 bar and shall propose an interpretation of all the atmospheric pressure results based on the possible coexistence of these two superconducting phases.