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Herschel-ATLAS and ALMA: HATLAS J142935.3-002836, a lensed major merger at redshift 1.027

[Abridged] Aims: This work focuses on one lensed system, HATLAS J142935.3-002836 (H1429-0028), selected in the Herschel-ATLAS field. Gathering a rich, multi-wavelength dataset, we aim to confirm the lensing hypothesis and model the background source's morphology and dynamics, as well as to provide a full physical characterisation. Methods: Multi-wavelength high-resolution data is utilised to assess the nature of the system. A lensing-analysis algorithm which simultaneously fits different wavebands is adopted to characterise the lens. The background galaxy dynamical information is studied by reconstructing the 3-D source-plane of the ALMA CO(J:4-3) transition. Near-IR imaging from HST and Keck-AO allows to constrain rest-frame optical photometry independently for the foreground and background systems. Physical parameters (such as stellar and dust masses) are estimated via modelling of the spectral energy distribution taking into account source blending, foreground obscuration, and differential magnification. Results: The system comprises a foreground edge-on disk galaxy (at z_sp=0.218) with an almost complete Einstein ring around it. The background source (at z_sp=1.027) is magnified by a factor of ~8-10 depending on wavelength. It is comprised of two components and a tens of kpc long tidal tail resembling the Antennae merger. As a whole, the system is a massive stellar system (1.32[-0.41,+0.63] x1E11 Mo) forming stars at a rate of 394+-90 Mo/yr, and has a significant gas reservoir M_ISM = 4.6+-1.7 x1E10 Mo. Its depletion time due to star formation alone is thus expected to be tau_SF=M_ISM/SFR=117+-51 Myr. The dynamical mass of one of the components is estimated to be 5.8+-1.7 x1E10 Mo, and, together with the photometric total mass estimate, it implies that H1429-0028 is a major merger system (1:2.8[-1.5,+1.8]).