Photonic memory is an important building block to delay, route and buffer optical information, for instance in optical interconnects or for recurrent optical signal processing. Photonic-phononic memory based on stimulated Brillouin-Mandelstam scattering (SBS) has been demonstrated as a coherent optical storage approach with broad bandwidth, frequency selectivity and intrinsic nonreciprocity. Here, we experimentally demonstrated the storage of quadrature-phase encoded data at room temperature and at cryogenic temperatures. We store and retrieve the 2-bit states \(\{00, 01, 10, 11\}\) encoded as optical pulses with the phases \(\{0, {\pi}/2 , {\pi}, 3{\pi}/2\}\) - a quadrature phase shift keying (QPSK) signal. The 2-bit signals are retrieved from the acoustic domain with a global phase rotation of \({\pi}\), which is inherent in the process due to SBS. We also demonstrate full phase control over the retrieved data based on two different handles: by detuning slightly from the SBS resonance, or by changing the storage time in the memory scheme we can cover the full range \([0, 2{\pi})\). At a cryogenic temperature of 3.9 K, we have increased readout efficiency as well as gained access to longer storage times, which results in a detectable signal at 140 ns. All in all, the work sets the cornerstone for optoacoustic memory schemes with phase-encoded data