  Context. The origin of water in the stratospheres of Giant Planets has been
an outstanding question ever since its first detection by ISO some 20 years
ago. Water can originate from interplanetary dust particles, icy rings and
satellites and large comet impacts. Analysis of Herschel Space Observatory
observations have proven that the bulk of Jupiter's stratospheric water was
delivered by the Shoemaker-Levy 9 impacts in 1994. In 2006, the Cassini mission
detected water plumes at the South Pole of Enceladus, placing the moon as a
serious candidate for Saturn's stratospheric water. Further evidence was found
in 2011, when Herschel demonstrated the presence of a water torus at the
orbital distance of Enceladus, fed by the moon's plumes. Finally, water falling
from the rings onto Saturn's uppermost atmospheric layers at low latitudes was
detected during the final orbits of Cassini's end-of-mission plunge into the
atmosphere. Aims. In this paper, we use Herschel mapping observations of water
in Saturn's stratosphere to identify its source. Methods. Several empirical
models are tested against the Herschel-HIFI and -PACS observations, which were
collected on December 30, 2010, and January 2nd, 2011 (respectively). Results.
We demonstrate that Saturn's stratospheric water is not uniformly mixed as a
function of latitude, but peaking at the equator and decreasing poleward with a
Gaussian distribution. We obtain our best fit with an equatorial mole fraction
1.1 ppb and a half-width at half-maximum of 25{\deg}, when accounting for a
temperature increase in the two warm stratospheric vortices produced by
Saturn's Great Storm of 2010-2011. Conclusions. This work demonstrates that
Enceladus is the main source of Saturn's stratospheric water.
