  We report three additional SINFONI detections of H-alpha emission line from
quasar absorbers, two of which are new identifications. These were targeted
among a sample of systems with log N(HI)>19.0 and metallicities measured from
high-resolution spectroscopy. The detected galaxies are at impact parameters
ranging from 6 to 12 kpc from the quasar's line-of-sight. We derive star
formation rates (SFR) of a few solar masses per year for the two absorbers at
z_abs~1 and SFR=17 solar masses per year for the DLA at z_abs~2. These three
detections are found among a sample of 16 DLAs and sub-DLAs (5 at z_abs~1 and 7
at z_abs~2). For the remaining undetected galaxies, we derive flux limits
corresponding to SFR<0.1--11.0 solar masses per year depending on redshift of
the absorber and depth of the data. When combined with previous results from
our survey for galaxy counterparts to HI-selected absorbers, we find a higher
probability of detecting systems with higher metallicity as traced by dust-free
[Zn/H] metallicity. We also report a higher detection rate with SINFONI for
host galaxies at z_abs~1 than for systems at z_abs~2. Using the NII/H-alpha
ratio, we can thus compare absorption and emission metallicities in the same
high-redshift objects, more than doubling the number of systems for which such
measures are possible.
