The HyperScout-H (HS-H) instrument is one of the payloads aboard ESA's Hera spacecraft. Hera is a planetary defence mission that aims to provide a detailed characterization of the near-Earth binary asteroid (65803) Didymos-Dimorphos after the NASA/DART mission impact. HS-H is a versatile dual-use payload, functioning as a hyperspectral imager that captures both images and spectral data within the 0.65─0.95 μm wavelength range. The observations from this instrument will offer key insights regarding the composition of the two bodies Didymos and Dimorphos, space weathering effects, and the potential presence of exogenous material on these asteroids. Thanks to its wide field of view (≍15.5∘×8.3∘ in paraxial approximation), HS-H will be able to monitor the system's orbital dynamic and dust environment, while both components of this binary asteroid remain in the field of view for most of the asteroid phase of the mission. These results also complement the data obtained from other instruments in characterizing the geomorphological units. The data that will be obtained by HS-H will enable the creation of maps highlighting key spectral features, such as taxonomic classification, spectral slope, and band parameters. This article presents the pre-flight calibration of the instrument, outlines the science objectives, and discusses the expected investigations. The instrument's capabilities are demonstrated through laboratory observations of two meteorite samples and a dedicated software toolbox was developed specifically for processing the instrument's data.