Treatment quality assessment is a crucial feature for both present and nextgeneration ion therapy facilities. Several approaches are being explored, based on prompt radiation emission or on PET signals by β+;-decaying isotopes generated by beam interactions with the body. In-beam PET monitoring at synchrotron-based ion therapy facilities has already been performed, either based on inter-spill data only, to avoid the influence of the prompt radiation, or including both in-spill and inter-spill data. However, the PET images either suffer of poor statistics (inter-spill) or are more influenced by the background induced by prompt radiation (in-spill). Both those problems are expected to worsen for accelerators with improved duty cycle where the inter-spill interval is reduced to shorten the treatment time. With the aim of assessing the detector performance and developing techniques for background reduction, a test of an in-beam PET detector prototype was performed at the CNAO synchrotron-based ion therapy facility in full-beam acquisition modality. Data taken with proton beams impinging on PMMA phantoms showed the system acquisition capability and the resulting activity distribution, separately reconstructed for the in-spill and the inter-spill data. The coincidence time resolution for in-spill and inter-spill data shows a good agreement, with a slight deterioration during the spill. The data selection technique allows the identification and rejection of most of the background originated during the beam delivery. The activity range difference between two different proton beam energies (68 and 72 MeV) was measured and found to be in submillimeter agreement with the expected result. However, a slightly longer (2 mm) absolute profile length is obtained for in-spill data when compared to inter-spill data.