  Molecular mapping is a supervised method exploiting the spectral diversity of
integral field spectrographs to detect and characterize resolved exoplanets
blurred into the stellar halo. We present an evolution of the method to remove
the stellar halo and the nuisance of telluric features in the datacubes and
access a continuum-subtracted spectra of the planets at R$\sim$4000. We derive
planet atmosphere properties from a direct analysis of the planet
telluric-corrected absorption spectrum. We applied our methods to the SINFONI
observation of the planet $\beta$ Pictoris b. We recover the CO and H$_2$O
detections in the atmosphere of $\beta$ Pic b using molecular mapping. We
further determine some basic properties of its atmosphere, with
$T_\text{eq}=1748^{+3}_{-4}$ K, a sub-solar [Fe/H]=$-0.235^{+0.015}_{-0.013}$
dex, and a solar C/O=$0.551 \pm 0.002$ in contrast with values measured for the
same exoplanet with other infrared instruments. We confirm a low projected
equatorial velocity of 25$^{+5}_{-6}$ km s$^{-1}$. We are also able to measure,
for the first time with a medium-resolution spectrograph, the radial velocity
of $\beta$ Pic b relative to the central star at MJD=56910.38 with a km/s
precision of $-11.3 \pm 1.1$ km s$^{-1}$, compatible with ephemerides based on
the current knowledge of the $\beta$ Pic system.
