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Close-up view of a luminous star-forming galaxy at z=2.95

(Abridged) Exploiting the sensitivity and broad band width of NOEMA, we have studied the molecular gas and dust in the galaxy HerBS-89a, at z=2.95. High angular resolution images reveal a partial 1.0" diameter Einstein ring in the dust continuum emission and the molecular emission lines of 12CO(9-8) and H2O(2_02-1_11). We report the detection of the three fundamental transitions of the molecular ion OH+, seen in absorption; the molecular ion CH+(1-0) seen in absorption (and tentatively in emission); two transitions of amidogen (NH2), seen in emission; and HCN(11-10) and/or NH(1_2-0_1) seen in absorption. The NOEMA data are complemented with VLA data tracing the 12CO(1-0) emission line, which provides a measurement of the total mass of molecular gas and an anchor for a CO excitation analysis. In addition, we present HST imaging that reveals the foreground lensing galaxy in the near-infrared. Together with data from the GTC, we derive a photometric redshift of z(phot)~0.9 for the foreground lensing galaxy. Modelling the lensing of HerBS-89a, we reconstruct the dust continuum and molecular emission lines (magnified by a factor ~4-5) in the source plane. The 12CO(9-8) and H2O emission lines have comparable spatial and kinematic distributions; the source-plane reconstructions do not clearly distinguish between a one-component and a two-component scenario, but the latter accounts for the observed broad line widths. HerBS-89a is a powerful star forming galaxy with a dust-to-gas ratio delta(GDR)~80, a SFR = 614 +/- 59 Msun/yr and a depletion timescale tau(depl) = (3.4 +/- 1.0) 1e8 years. The OH+ and CH+ absorption lines, all have their main velocity component red-shifted by Δ(V)~100 km/s relative to the global CO reservoir. We argue that these absorption lines trace a rare example of gas inflow towards the center of the galaxy.