The recent interest in positrons distribution in the space revealed the anomalous presence of high energetic positrons. There are different possible origins of such positrons, including the decay of heavy particles in the dark matter, also pulsars or neutron stars. In our study we calculated the annihilation properties of the electron – positron bound system in superstrong magnetic fields expected for neutron stars. For this aim we use solutions of the (relativistic) Bethe-Salpeter equation derived by L.B. Leinson and A. Perez . The results indicate strong dependency of the annihilation properties (rate and intensity) on the value of the magnetic field.