  We report on the first NuSTAR observation of the transitional millisecond
pulsar binary XSS J12270-4859 during its current rotation-powered state,
complemented with a 2.5yr-long radio monitoring at Parkes telescope and
archival XMM-Newton and Swift X-ray and optical data. The radio pulsar is
mainly detected at 1.4GHz displaying eclipses over about 40% of the 6.91h
orbital cycle. We derive a new updated radio ephemeris to study the 3-79keV
light curve that displays a significant orbital modulation with fractional
amplitude of 28+/-3%, a structured maximum centred at the inferior conjunction
of the pulsar and no cycle-to-cycle or low-high-flaring mode variabilities. The
average X-ray spectrum, extending up to about 70keV without a spectral break,
is well described by a simple power-law with photon index Gamma = 1.17+/-0.08
giving a 3-79keV luminosity of 7.6(-0.8;+3.8)x10**32 erg/s, for a distance of
1.37(-0.15;+0.69)kpc. Energy resolved orbital light curves reveal that the
modulation is not energy dependent from 3keV to 25keV and is undetected with an
upper limit of about 10% above 25keV. Comparison with previous X-ray XMM-Newton
observations in common energy ranges confirms that the modulation amplitudes
vary on timescales of a few months, indicative of a non-stationary contribution
of the intrabinary shock formed by the colliding winds of the pulsar and the
companion. A more detailed inspection of energy resolved modulations than
previously reported gives hints of a mild softening at superior conjunction of
the pulsar below 3keV, likely due to the contribution of the thermal emission
from the neutron star. The intrabinary shock emission, if extending into the
MeV range, would be energetically capable alone to irradiate the donor star.
