  We show that measuring the proper motion of ${{\sim 2000}}$ stars within a
dwarf galaxy, with an uncertainty of 1 km/s at most, can establish whether the
Dark Matter (DM) density profile of the dwarf has a central core or cusp. We
derive these limits by building mock star catalogues similar to those expected
from future astrometric {\it Theia}-like missions and including celestial
coordinates, radial velocity and proper motion of the stars. The density field
of the DM halo of the dwarf is sampled from an extended Navarro-Frank-White
(eNWF) spherical model, whereas the number density distribution of the stars is
a Plummer sphere. The velocity field of the stars is set according to the Jeans
equations. A Monte Carlo Markov Chain algorithm applied to a sample of
$N\gtrsim 2000$ stars returns unbiased estimates of the eNFW DM parameters
within $10\%$ of the true values and with $1\sigma$ relative uncertainties
$\lesssim 20$\%. The proper motions of the stars lift the degeneracy among the
eNFW parameters which appears when the line-of-sight velocities alone are
available. {Our analysis demonstrates that, by estimating the log-slope of the
mass density profile estimated at the half-light radius, a sample of $N=2000$
stars can distinguish between a core and a cusp at more than $8\sigma$.} Proper
motions also return unbiased estimates of the dwarf mass profile with $1\sigma$
uncertainties that decrease, on average, from 2.65 dex to 0.15 dex when the
size of the star sample increases from $N=100$ to $N=6000$ stars. The measure
of the proper motions can thus strongly constrain the distribution of DM in
nearby dwarfs and provides a fundamental contribution to understanding the
nature and the properties of DM.
