  Paper I presents the magnetic structure of a filament that developed in
active region (AR) NOAA 10781. In this paper we complement those results with
the velocities retrieved from Doppler shifts measured at the chromosphere and
the photosphere in the AR filament area. Various inversion methods with
different numbers of atmospheric components and different weighting schemes of
the Stokes profiles were used. The velocities were calibrated on an absolute
scale. A ubiquitous chromospheric downflow is found in the faculae surrounding
the filament, with an average velocity of 1.6 km/s. The filament region,
however, displays upflows in the photosphere on both days, when the linear
polarization (which samples the transverse component of the fields) is given
more weight in the inversions. The upflow speeds of the transverse fields in
the filament region average -0.15 km/s. In the chromosphere, the situation is
different for the two days of observation. On July 3, the chromospheric portion
of the filament is moving upwards as a whole with a mean speed of -0.24 km/s.
However, on July 5 only the section above an orphan penumbra shows localized
upflow patches, while the rest of the filament is dominated by the same
downflows observed elsewhere in the facular region. Photospheric supersonic
downflows that last for tens of minutes are detected below the filament, close
to the PIL.
  The observed velocity pattern in this AR filament strongly suggests a
scenario where the transverse fields are mostly dominated by upflows. The
filament flux rope is seen to be emerging at all places and both heights, with
a few exceptions in the chromosphere. This happens within a surrounding facular
region that displays a generalized downflow in the chromosphere and localized
downflows of supersonic character at the photosphere. No large scale downflow
of transverse field lines is observed at the photosphere.
