  We present a numerical study of the properties of the flow produced by the
collision of a magnetized anisotropic pulsar wind with the circumbinary
environment. We focus on studying the impact of the high wind magnetization on
the geometrical structure of the shocked flow. This work is an extension of our
earlier studies that focused on a purely hydrodynamic interaction and weak wind
magnetization. We consider the collision in the axisymmetric approximation,
that is, the pulsar rotation axis is assumed to be oriented along the line
between the pulsar and the optical star. The increase of the magnetization
results in the expansion of the opening cone in which the shocked pulsar wind
propagates. This effect is explained in the frameworks of the conventional
theory of collimation of magnetized winds. This finding has a direct
implication for scenarios that involve Doppler boosting as the primary
mechanism behind the GeV flares detected with the Fermi/LAT from PSR
B1259-63/LS2883. The maximum enhancement of the apparent emission is determined
by the ratio of $4\pi$ to the solid in which the shocked pulsar wind
propagates. Our simulations suggest that this enhancement factor is decreased
by the impact of the magnetic field.
