We present accurate results for optical conductivity of the three dimensional Fröhlich polaron in all coupling regimes. The systematic-error free diagrammatic quantum Monte Carlo method is employed where the Feynman graphs for the momentum-momentum correlation function in imaginary time are summed up. The real-frequency optical conductivity is obtained by the analytic continuation with stochastic optimization. We compare numerical data with available perturbative and nonperturbative approaches to the optical conductivity and show that the picture of sharp resonances due to relaxed excited states in the strong-coupling regime is "washed out" by large broadening of these states. As a result, the spectrum contains only a single-maximum broad peak with peculiar shape and a shoulder.