Context : Paper I presents the magnetic structure , inferred for the photosphere and the chromosphere , of a filament that developed in active region ( AR ) NOAA 10781 , observed on 2005 July 3 and July 5 .

Aims : 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 .

Methods : The velocities and magnetic field parameters were inferred from full Stokes inversions of the photospheric Si i 10827 Å line and the chromospheric He i 10830 Å triplet .
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 .

Results : A ubiquitous chromospheric downflow is found in the faculae surrounding the filament , with an average velocity of 1.6 km s ^ { -1 } .
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 ^ { -1 } .
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 ^ { -1 } .
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 .

Conclusions : 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 .