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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.