We present the results of \sim 2.5 years AGILE Â observations of PSR B1509–58and of the same interval of Fermi -LATÂ observations . The modulation significance of AGILE Â light-curve above 30 MeV is at a 5 \sigma confidence level and the light-curve shows a broad asymmetric first peak reaching its maximum 0.39 \pm 0.02 cycles after the radio peak plus a second peak at 0.94 \pm 0.03 . The gamma-ray spectral energy distribution of pulsed flux is well described by a power-law ( photon index \alpha = 1.87 \pm 0.09 ) with a remarkable cutoff at E _ { c } = 81 \pm 20 Â MeV , representing the softest spectrum observed among \gamma -ray pulsars so far . The unusual soft break in the spectrum of PSR B1509–58Â has been interpreted in the framework of polar cap models as a signature of the exotic photon splitting process in the strong magnetic field of this pulsar . In the case of an outer-gap scenario , or the two pole caustic model , better constraints on the geometry of the emission would be needed from the radio band in order to establish whether the conditions required by the models to reproduce AGILE Â light-curves and spectra match the polarization measurements .