  Outflows driven by active galactic nuclei (AGN) are expected to have a
significant impact on the host galaxy evolution, but it is still debated how
they are accelerated and propagate on galaxy-wide scales. This work addresses
these questions by studying the link between X-ray, nuclear ultra-fast outflows
(UFOs) and extended ionised outflows, for the first time in two quasars close
to the peak of AGN activity ($z\sim2$), where AGN feedback is expected to be
more effective. As targets, we selected two multiple-lensed quasars at
$z\sim1.5$, HS 0810+2554 and SDSS J1353+1138, known to host UFOs and observed
with the near-IR integral field spectrometer SINFONI at the VLT. We performed a
kinematical analysis of the [O III]$\lambda$5007 optical emission line, in
order to trace the presence of ionised outflows. We detected spatially resolved
ionised outflows in both galaxies, extended more than 8 kpc and moving up to
$v>2000$ km/s. We derived mass outflow rates of $\sim$12 M$_{sun}$/yr and
$\sim$2 M$_{sun}$/yr for HS 0810+2554 and SDSS J1353+1138. Comparing with the
co-hosted UFO energetics, the ionised outflow energetics in HS 0810+2554 is
broadly consistent with a momentum-driven regime of wind propagation, while in
SDSS J1353+1138 it differs by a factor of $\sim$100 from theoretical
predictions, requiring either a massive molecular outflow or a high variability
of the AGN activity to account for such a discrepancy. By additionally
considering our results with those from the small sample of well-studied
objects (all local but one), with both UFO and extended
(ionised/atomic/molecular) outflow detections, we found that in 10 out of 12
galaxies the large-scale outflow energetics is consistent with the theoretical
predictions of either a momentum- or an energy-driven scenario. This suggests
that such models explain relatively well the acceleration mechanism of
AGN-driven winds on large scales.
