(abridged) The HH 80/81/80N jet extends from the HH 80 object to the recently discovered Source 34 and has a total projected jet size of 10.3 pc, constituting the largest collimated radio-jet system known so far. It is powered by IRAS 18162-2048 associated with a massive young stellar object. We report 6 cm JVLA observations that, compared with previous 6 cm VLA observations carried out in 1989, allow us to derive proper motions of the HH 80, HH 81 and HH 80N radio knots located about 2.5 pc away in projection from the powering source. For the first time, we measure proper motions of the optically obscured HH 80N object providing evidence that HH 81, 80 and 80N are associated with the same radio-jet. We derived tangential velocities of these HH objects between 260 and 350 km/s, significantly lower than those for the radio knots of the jet close to the powering source (600-1400 km/s) derived in a previous work, suggesting that the jet material is slowing down due to a strong interaction with the ambient medium. The HH 80 and HH 80N emission at 6 cm is, at least in part, probably synchrotron radiation produced by relativistic electrons in a magnetic field of 1 mG. If these electrons are accelerated in a reverse adiabatic shock, we estimate a jet total density of $lesssim1000$ cm$^{-3}$. All these features are consistent with a jet emanating from a high mass protostar and make evident its capability of accelerating particles up to relativistic velocities.
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