  The process of electron-positron pair production by a photon with subsequent
annihilation to a single photon in a strong magnetic field has been studied.
The general amplitude has been calculated and the process rate have been found
in the low Landau levels approximation (resonant and nonresonant cases). The
comparison of resonant and nonresonant cases shows a significant excess of the
resonant rate. The polarization of the final photon in a strong magnetic field
has also been found. It has been shown that polarizations of the initial and
the final photons are independent except for the case of normal linear
polarization of the initial photon.
