  Prestellar cores, the birthplace of Sun-like stars, form from the
fragmentation of the filamentary structure that composes molecular clouds, from
which they must inherit at least partially the kinematics. Furthermore, when
they are on the verge of gravitational collapse, they show signs of subsonic
infall motions. How extended these motions are, which depends on how the
collapse occurs, remains largely unknown. We want to investigate the kinematics
of the envelope that surrounds the prototypical prestellar core L1544, studying
the cloud-core connection. To our aims, we observed the $\rm HCO^+$(1-0)
transition in a large map. \hcop is expected to be abundant in the envelope,
making it an ideal probe of the large-scale kinematics in the source. We
modelled the spectrum at the dust peak by means of a non
local-thermodynamical-equilibrium radiative transfer. In order to reproduce the
spectrum at the dust peak, a large ($\sim 1\, \rm pc$) envelope is needed, with
low density (tens of $\rm cm^{-3}$ at most) and contraction motions, with an
inward velocity of $\approx 0.05\,\rm km \, s^{-1}$. We fitted the data cube
using the Hill5 model, which implements a simple model {for the optical depth
and excitation temperature profiles along the line-of-sight,} in order to
obtain a map of the infall velocity. This shows that the infall motions are
extended, with typical values in the range $0.1-0.2\,\rm km \, s^{-1}$. Our
results suggest that the contraction motions extend in the diffuse envelope
surrounding the core, which is consistent with recent magnetic field
measurements in the source, which showed that the envelope is magnetically
supercritical.
