  A supersolid is a fascinating phase of matter, combining the global phase
coherence of a superfluid with hallmarks of solids, e.g. a spontaneous breaking
of the translational symmetry. Recently, states with such counter-intuitive
properties have been realized in experiments using ultracold quantum gases with
strong dipolar interactions. Here, we investigate the response of a supersolid
state to phase excitations which shatter the global phase coherence. After the
creation of those excitations, we observe a rapid re-establishment of a global
phase coherence, suggesting the presence of a superfluid flow across the whole
sample and an efficient dissipation mechanism. We are able to identify a
well-defined region where rephasing occurs, indicating the phase boundary
between the solid-like and the supersolid phase. Our observations call for the
development of theoretical descriptions able to capture the non-equilibrium
dynamics in the recently discovered supersolid states of quantum matter.
