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In this work we perform a detailed theoretical and experimental investigation of an atomic memory based on recoil-induced resonance in cold cesium atoms. We consider the interaction of a nearly degenerated pump and probe beams with an ensemble of two-level atoms. A full theoretical density matrix calculation in the extended Hilbert space of the internal and external atomic degrees of freedom allows us to obtain, from first principles, the transient and stationary responses determining the probe transmission and the forward four-wave mixing spectra. These two signals are generated together at the same order of perturbation with respect to the intensities of pump and probe beams. However, during continuous excitation of the sample, they are detected in very different ways and the signal at the probe transmission appears to be considerably larger, being the main focus of investigation prior to this work. Moreover, we have investigated the storage of optical information in the atomic external degrees of freedom, which provided a simple interpretation for the previously-reported non-volatile character of this memory. The retrieved signals after storage reveal the equivalent role of probe transmission and four-wave mixing, as the two signals have similar amplitudes. Probe transmission and forward four-wave-mixing spectra were then experimentally measured for both continuous excitation and after storage. The experimental observations are in good agreement with the developed theory and open a new pathway for the reversible exchange of optical information with atomic systems.