We performed a first-principles study of the structural, vibrational, electronic and magnetic properties of NaMnF3 under applied isotropic pressure. We found that NaMnF3 undergoes a reconstructive phase transition at 8 GPa from the Pnma distorted perovskite structure toward the Cmcm post-perovskite structure. This is confirmed by a sudden change of the Mn-F-Mn bondings where the crystal goes from corner shared octahedra in the Pnma phase to edge shared octahedra in the Cmcm phase. The magnetic ordering also changes from a G-type antiferromagnetic ordering in the Pnma phase to a C-type antiferromagnetic ordering in the Cmcm phase. Interestingly, we found that the high-spin d-orbital filling is kept at the phase transition which has never been observed in the known magnetic post-perovskite structures. We also found a highly non-collinear magnetic ordering in the Cmcm post-perovskite phase that drives a large ferromagnetic canting of the spins. We discuss the validity of these results with respect to the U and J parameter of the GGA+U exchange correlation functional used in our study and conclude that large spin canting is a promising property of the post-perovskite fluoride compounds.