  We apply a statistical deconvolution of the parallax errors based on Lucy's
inversion method (LIM) to the Gaia-DR3 sources to measure their three
dimensional velocity components in the range of Galactocentric distances $R$
between 8 kpc and 30 kpc with their corresponding errors and root mean square
values. We find results that are consistent with those obtained by applying LIM
to the Gaia-DR2 sources, and we conclude that the method gives convergent and
more accurate results by improving the statistics of the data-set and lowering
observational errors. The kinematic maps reconstructed with LIM up to $R
\approx 30$ kpc show that the Milky Way is characterized by asymmetrical
motions with significant gradients in all velocity components. Furthermore, we
determine the Galaxy rotation curve $V_C(R)$ up to $\approx 27.5$ kpc with the
cylindrical Jeans equation assuming an axisymmetric gravitational potential. We
find that $V_C(R)$ is significantly declining up to the largest radius
investigated. Finally, we also measure $V_C(R)$ at different vertical heights,
showing that, for $R <15$ kpc, there is a marked dependence on $Z$, whereas at
larger $R$ the dependence on $Z$ is negligible.
