GJ758 B is a brown dwarf companion to a nearby (15.76 pc) solar-type, metal-rich (M/H = +0.2 dex) main-sequence star (G9V) that was discovered with Subaru/HiCIAO in 2009. From previous studies, it has drawn attention as being the coldest (~600K) companion ever directly imaged around a neighboring star. We present new high-contrast data obtained during the commissioning of the SPHERE instrument at the VLT. The data was obtained in Y-, J-, H-, and Ks-bands with the dual-band imaging (DBI) mode of IRDIS, providing a broad coverage of the full near-infrared (near-IR) range at higher contrast and better spectral sampling than previously reported. In this new set of high-quality data, we report the re-detection of the companion, as well as the first detection of a new candidate closer-in to the star. We use the new 8 photometric points for an extended comparison of GJ758 B with empirical objects and 4 families of atmospheric models. From comparison to empirical object, we estimate a T8 spectral type, but none of the comparison object can accurately represent the observed near-IR fluxes of GJ758 B. From comparison to atmospheric models, we attribute a Teff = 600K $pm$ 100K, but we find that no atmospheric model can adequately fit all the fluxes of GJ758 B. The photometry of the new candidate companion is broadly consistent with L-type objects, but a second epoch with improved photometry is necessary to clarify its status. The new astrometry of GJ758 B shows a significant proper motion since the last epoch. We use this result to improve the determination of the orbital characteristics using two fitting approaches, Least-Square Monte Carlo and Markov Chain Monte Carlo. Finally, we analyze the sensitivity of our data to additional closer-in companions and reject the possibility of other massive brown dwarf companions down to 4-5 AU. [abridged]
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