In this paper, we examined a possibility of preservation of a substantially multimode radiation in a single cell of quantum memory. As a light source we considered a synchronously pumped optical parametric oscillator (SPOPO). As was shown in several studies, SPOPO radiation has a large number of the correlated modes making it attractive for the purposes of quantum communication and computing. We showed that these correlations can be mapped on the longitudinal spin waves of the memory cell and be restored later in the readout light. The efficiencies of the writing and readout depend on the mode structure of the memory determined by a mechanism of the light-matter interaction under consideration (the nonresonance Raman interaction) and by the profile of the driving light field. We showed that like the initial light pulse train, the restored one can be represented by a set of squeezed supermodes. The mapping of the quantum multimode correlations on the material medium offers opportunities to manipulate the quantum states within the memory cell followed by the reading of the transformed state.