A study of "inverted" core-shell, MnO/γ-Mn2O3, nanoparticles is presented. Crystal and magnetic structures and characteristic sizes have been determined by neutron diffraction for the antiferromagnetic core (MnO) and the ferrimagnetic shell (γ-Mn2O3). Remarkably, while the MnO core is found to have a TN not far from its bulk value, the magnetic order of the γ-Mn2O3 shell is stable far above TC, exhibiting two characteristic temperatures, at T~ 40  K [TC(γ-Mn2O3)] and at T~120  K [~ TN(MnO)]. Magnetization measurements are consistent with these results. The stabilization of the shell moment up to TN of the core can be tentatively attributed to core-shell exchange interactions, hinting at a possible magnetic proximity effect.