We derive the cross-section for one-quantum annihilation of polarized elect
rons and positrons. The electron and positron can occupy arbitrary Landau l
evels and have non-zero momentum parallel to the field, and the cross-secti
on is calculated for any polarization of the radiation. When we take zero p
arallel momentum for the electron and sum over photon polarization we obtai
n results which agree with the existing calculation of Wunner et al. (1986)
.