  Spectropolarimetric reconstructions of the photospheric vector magnetic field
are intrinsically limited by the 180$^\circ$-ambiguity in the orientation of
the transverse component. So far, the removal of such an ambiguity has required
assumptions about the properties of the photospheric field, which makes
disambiguation methods model-dependent. The basic idea is that the unambiguous
line-of-sight component of the field measured from one vantage point will
generally have a non-zero projection on the ambiguous transverse component
measured by the second telescope, thereby determining the ``true'' orientation
of the transverse field. Such an idea was developed and implemented in the
Stereoscopic Disambiguation Method (SDM), which was recently tested using
numerical simulations. In this work we present a first application of the SDM
to data obtained by the High Resolution Telescope (HRT) onboard Solar Orbiter
during the March 2022 campaign, when the angle with Earth was 27 degrees. The
method is successfully applied to remove the ambiguity in the transverse
component of the vector magnetogram solely using observations (from HRT and
from the Helioseismic and Magnetic Imager), for the first time. The SDM is
proven to provide observation-only disambiguated vector magnetograms that are
spatially homogeneous and consistent. A discussion about the sources of error
that may limit the accuracy of the method, and of the strategies to remove them
in future applications, is also presented.
