The study of the entanglement dynamics plays a fundamental role in\nunderstanding the behaviour of many-body quantum systems out of equilibrium. In\nthe presence of a globally conserved charge, further insights are provided by\nthe knowledge of the resolution of entanglement in the various symmetry\nsectors. Here, we carry on the program we initiated in [Phys. Rev. B 103,\nL041104 (2021)], for the study of the time evolution of the symmetry resolved\nentanglement in free fermion systems. We complete and extend our derivations\nalso by defining and quantifying a symmetry resolved mutual information. The\nentanglement entropies display a time delay that depends on the charge sector\nthat we characterise exactly. Both entanglement entropies and mutual\ninformation show effective equipartition in the scaling limit of large time and\nsubsystem size. Furthermore, we argue that the behaviour of the charged\nentropies can be quantitatively understood in the framework of the\nquasiparticle picture for the spreading of entanglement, and hence we expect\nthat a proper adaptation of our results should apply to a large class of\nintegrable systems. We also find that the number entropy grows logarithmically\nwith time before saturating to a value proportional to the logarithm of the\nsubsystem size.\n