We present UV to NIR spectroscopic observations of the quasar J0015+1842 and its proximate molecular absorber at z=2.631. The [OIII] emission line of the quasar is composed of a broad (FWHM~1600 km/s), spatially-unresolved component, blueshifted by ~600 km/s from a narrow, spatially-resolved component (FWHM~650 km/s). The wide, blueshifted, unresolved component is consistent with the presence of outflowing gas in the nuclear region. The narrow component can be further decomposed into a blue and a red blob with velocity width of several hundred km/s each, seen ~5 pkpc on opposite spatial locations from the nuclear emission, indicating outflows over galactic scales. The presence of ionised gas over kpc-scales is also seen from a weak CIV emission component, detected in the trough of a saturated CIV absorption that removes the strong nuclear emission from the quasar. Towards the nuclear emission, we observe absorption lines from atomic species in various ionisation and excitation stages and confirm the presence of strong H2 lines. The overall absorption profile is very wide, spread over ~600 km/s, roughly matching in velocities the blue narrow [OIII] blob. From detailed investigation of the chemical and physical conditions in the absorbing gas, we infer densities of about nH ~ 10^4-10^5 cm^-3 in the cold (T~100 K) H2-bearing gas, which we find to be located at ~10 kpc distances from the central UV source. We conjecture that we are witnessing different manifestations of a same AGN-driven multi-phase outflow, where approaching gas is intercepted by the line of sight to the nucleus. We corroborate this picture by modelling the scattering of Ly-a photons from the central source through the outflowing gas, reproducing the peculiar Ly-a absorption-emission profile, with a damped Ly-a absorption in which red-peaked, spatially offset and extended Ly-a emission is seen. [abridged]
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