We aim to characterise the morphology and the physical parameters governing the shock physics of the Herbig-Haro object HH99B. We have obtained SINFONI-SPIFFI IFU spectroscopy between 1.10 and 2.45 um detecting more than 170 emission lines, Most of them come from ro-vibrational transitions of H_2 and [FeII]. All the brightest lines appear resolved in velocity. Intensity ratios of ionic lines have been compared with predictions of NLTE models to derive bi-dimensional maps of extinction and electron density, along with estimates of temperature, fractional ionisation and atomic hydrogen post-shock density. H_2 line intensities have been interpreted in the framework of Boltzmann diagrams, from which we have derived maps of extinction and temperature of the molecular gas. From the intensity maps of bright lines the kinematical properties of the shock(s) at work in the region have been delineated. Finally, from selected [FeII] lines, constraints on the spontaneous emission coefficients of the 1.257, 1.321 and 1.644 um lines are provided. The kinematical properties derived for the molecular gas substantially confirm those published in Davis et al.(1999), while new information (e.g. v_shock ~115 km s^-1 is provided for the shock component responsible for the ionic emission. We also provide an indirect measure of the H_2 breakdown speed (between 70 and 90 km s^-1) and compute the inclination angle with respect to the line of sight. The map parameters, along with images of the observed line intensities, will be used to put stringent constraints on up-to-date shock models.
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