  We analyze JWST NIRSpec$+$MIRI/MRS observations of the infrared (IR)
gas-phase molecular bands of the most enshrouded source (D1) within the
interacting system and luminous IR galaxy II Zw 096. We report the detection of
rovibrational lines of H$_2$O $\nu_2$=1-0 ($\sim$5.3-7.2 $\mu$m) and $^{12}$CO
$\nu$=1-0 ($\sim$4.45-4.95 $\mu$m) in D1. The CO band shows the R- and
P-branches in emission and the spectrum of the H$_2$O band shows the P-branch
in emission and the R-branch in absorption. The H$_2$O R-branch in absorption
unveils an IR-bright embedded compact source in D1 and the CO broad component
features a highly turbulent environment. From both bands, we also identified
extended intense star-forming (SF) activity associated with circumnuclear
photodissociation regions (PDRs), consistent with the strong emission of the
ionised 7.7 $\mu$m polycyclic aromatic hydrocarbon band in this source. By
including the 4.5-7.0 $\mu$m continuum information derived from the H$_2$O and
CO analysis, we modelled the IR emission of D1 with a dusty torus and SF
component. The torus is very compact (diameter of $\sim$3 pc at 5 $\mu$m) and
characterised by warm dust ($\sim$ 370 K), giving an IR surface brightness of
$\sim$3.6$\times$10$^{8}$ L$_{\rm sun}$/pc$^2$. This result suggests the
presence of a dust-obscured active galactic nucleus (AGN) in D1, which has an
exceptionally high covering factor that prevents the direct detection of AGN
emission. Our results open a new way to investigate the physical conditions of
inner dusty tori via modelling the observed IR molecular bands.
