The flux of unstable secondary cosmic ray nuclei, produced by spallation processes in the interstellar medium, can be used to constrain the residence time of cosmic rays inside the Galaxy. Among them, $^{10}$Be is especially useful because of its relatively long half-life of 1.39 Myr... In the framework of the diffusive halo model we describe cosmic ray transport taking into account all relevant interaction channels and accounting for the decay of unstable secondary nuclei. We then compare our results with the data collected by the Alpha Magnetic Spectrometer (AMS-02) on board the International Space Station for the flux ratios Be/C, B/C, Be/O, B/O, C/O and Be/B as well as C, N and O absolute fluxes. These measurements, and especially the Be/B ratio, allow us to single out the flux of $^{10}$Be and infer a best fit propagation time of CRs in the Galaxy. Our results show that, if the cross sections for the production of secondary elements through spallation are taken at face value, AMS-02 measurements are compatible with the standard picture based on CR diffusion in a halo of size $H \gtrsim 5$ kpc. Taking into account the uncertainties in the cross sections, this conclusion becomes less reliable, although still compatible with the standard picture. Implications of our findings for alternative models of CR transport are discussed. (read more)