We study the effect a guiding magnetic field has on the formation and structure of a pair jet that propagates through a collisionless electron-proton plasma at rest. We model with a PIC simulation a pair cloud with the temperature 400 keV and mean speed 0.9c. The cloud propagates through a spatially uniform, magnetized and cool ambient electron-proton plasma that is at rest. Its mean velocity vector is aligned with the background magnetic field. A jet forms in time. Its outer cocoon consists of jet-accelerated ambient plasma and is separated from the inner cocoon by an electromagnetic piston with a thickness that is comparable to the thermal gyroradius of jet particles. A supercritical fast magnetosonic shock will form between the pristine ambient plasma and the jet-accelerated one on a time scale that exceeds our simulation time by an order of magnitude. The inner cocoon is pair plasma that lost its directed flow energy while it swept out the background magnetic field. A beam of electrons and positrons moves along the jet spine at its initial speed. Its electrons are slowed down and some positrons are accelerated as they cross the jets head. The latter escape upstream along the magnetic field, which yields an excess of MeV positrons ahead of the jet. Some of the protons, which were located behind the electromagnetic piston at the time it formed, are accelerated to MeV energies
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