In heavy-ion therapy, the stopping position of primary ions in tumours needs to be monitored for effective treatment and to prevent overdose exposure to normal tissues. Positron-emitting ion beams, such as 11C and 15O, have been suggested for range verification in heavy-ion therapy using in-beam positron emission tomography (PET) imaging, which offers the capability of visualizing the ion stopping position with a high signal-To-noise ratio. We have previously demonstrated the feasibility of in-beam PET imaging for the range verification of 11C and 15O ion beams and observed a slight shift between the beam stopping position and the dose peak position in simulations, depending on the initial beam energy spread. In this study, we focused on the experimental confirmation of the shift between the Bragg peak position and the position of the maximum detected positron-emitting fragments via a PET system for positron-emitting ion beams of 11C (210 MeV u-1) and 15O (312 MeV u-1) with momentum acceptances of 5% and 0.5%. For this purpose, we measured the depth doses and performed in-beam PET imaging using a polymethyl methacrylate (PMMA) phantom for both beams with different momentum acceptances. The shifts between the Bragg peak position and the PET peak position in an irradiated PMMA phantom for the 15O ion beams were 1.8 mm and 0.3 mm for momentum acceptances of 5% and 0.5%, respectively. The shifts between the positions of two peaks for the 11C ion beam were 2.1 mm and 0.1 mm for momentum acceptances of 5% and 0.5%, respectively. We observed larger shifts between the Bragg peak and the PET peak positions for a momentum acceptance of 5% for both beams, which is consistent with the simulation results reported in our previous study. The biological doses were also estimated from the calculated relative biological effectiveness (RBE) values using a modified microdosimetric kinetic model (mMKM) and Monte Carlo simulation. Beams with a momentum acceptance of 5% should be used with caution for therapeutic applications to avoid extra dose to normal tissues beyond the tumour when the dose distal fall-off is located beyond the treatment volume.