This talk explores the dynamics of relativistic jets from binary neutron star (BNS) mergers, known to produce short Gamma-Ray Bursts (sGRBs). To accurately predict the afterglow emission, simulations should follow the jet evolution up to a nearly ballistic phase, where the angular structure has stabilized and the conversion of energy into kinetic form is almost complete. In order to capture this transition while retaining a 3D description, we extend previous magnetized jet simulations to a few tens of seconds after jet launching, avoiding any loss of resolution by remapping the jet from a spherical to a Cartesian grid. Our results reveal how energy conversion affects jet acceleration and angular structure, and offer reliable input for computing the corresponding afterglow light curves.