Positron range is a limiting factor in spatial resolution of positron emission tomography (PET) imaging. In this work we investigated the tissue-dependent nature of positron range and its effect on imaging with the new Biograph mMR 3 T whole-body PET/MR system. Positron range simulations were performed for Rb-82 and Ga-68 in homogeneous and non-homogeneous configurations of soft and lung tissue using Geant4. In addition, a 3D MLEM reconstruction framework was extended to incorporate correction kernels that compensate for the effect of positron range. We developed methods for selecting and adapting such correction kernels based on the MR-derived attenuation map and pre-simulated positron range data. The methods were evaluated using Monte Carlo (MC) simulation data on a model of the mMR system including the 3 T magnetic field (MF) and the MR body coil. The results prove that the use of tissue-specific positron range kernels results in better spatial resolution. Especially, the application of generalized kernels at the borders of different tissue types has the potential to provide better contrast and lesion localization.