  The gas content of galaxies is a key factor for their growth, starting from
star formation and black hole accretion to galaxy mergers. Thus, characterising
its properties via observations of tracers like the CO emission line is of big
importance in order to understand the bigger picture of galaxy evolution. We
present Atacama Large Millimeter/submillimeter Array (ALMA) observations of
dust continuum, CO(5-4) and CO(8-7) line emission in the quasar--star-forming
companion system SMM J04135+10277 (z=2.84). Earlier low-$J$ CO studies of this
system found a huge molecular gas reservoir associated to the companion galaxy,
while the quasar appeared gas-poor. Our CO observations revealed that the host
galaxy of the quasar is also gas-rich, with an estimated molecular gas mass of
$\sim(0.7-2.3)\times10^{10}$ M$_{\odot}$. The CO line profiles of the companion
galaxy are broad ($\sim1000$ km s$^{-1}$), and show signs of rotation of a
compact, massive system. In contrast to previous far-infrared observations, we
resolve the continuum emission and detect both sources, with the companion
galaxy dominating the dust continuum and the quasar having a $\sim25\%$
contribution to the total dust emission. By fitting the infrared spectral
energy distribution of the sources with \textsc{MR-MOOSE} and empirical
templates, the infrared luminosities of the quasar and the companion are in the
range of $L_{\rm IR, QSO}\sim(2.1-9.6)\times10^{12}$ L$_{\odot}$ and $L_{\rm
IR, Comp.}\sim(2.4-24)\times10^{12}$ L$_{\odot}$, while the estimated star
formation rates are $\sim210-960$ M$_{\odot}$ yr$^{-1}$ and $\sim240-2400$
M$_{\odot}$ yr$^{-1}$, respectively. Our results demonstrate that non-detection
of low-$J$ CO transition lines in similar sources does not necessarily imply
the absence of massive molecular gas reservoir but that the excitation
conditions favour the excitation of high-$J$ transitions.
