  Dynamical modelling of Integral-Field-Unit (IFU) stellar kinematics is a
powerful tool to unveil the dynamical structure and mass build-up of galaxies
in the local Universe, while gravitational lensing is nature's cosmic telescope
to explore the properties of galaxies beyond the local Universe. We present a
new approach which unifies dynamical modelling of galaxies with the
magnification power of strong gravitational lensing, to reconstruct the
structural and dynamical properties of high-redshift galaxies. By means of
axisymmetric Jeans modelling, we create a dynamical model of the source galaxy,
assuming a surface brightness and surface mass density profile. We then predict
how the source's surface brightness and kinematics would look like when lensed
by the foreground mass distribution and compare with the mock observed arcs of
strong gravitational lensing systems. For demonstration purposes, we create and
analyse mock data of the strong lensing system RX J1131-1231. By modelling both
the lens and source, we recover the dynamical mass within the effective radius
of strongly lensed high-redshift sources within 5% uncertainty, and we improve
the constraints on the lens mass parameters by up to 50%. This machinery is
particularly well suited for future observations from large segmented-mirror
telescopes, such as the James Webb Space Telescope, that will yield high
sensitivity and angular-resolution IFU data for studying distant and faint
galaxies.
