The Near Ultraviolet High Density (NUV-HD) SiPMs produced by Fondazione Bruno Kessler have been employed to develop 16-pixel optical units to equip the focal plane of the prototype Schwarzschild–Couder Telescope (pSCT) proposed as a possible design for the Medium-Sized Telescope of the Cherenkov Telescope Array Observatory. After the assembly procedure, the optical units were tested and characterized to study their performance and homogeneity in terms of gain and dark count rate. In this work, we report on the assembly procedure and on the laboratory tests performed on different production of NUV-HD and the selection we made for the best quality sensors to be used in the installation on the telescope camera. Currently 36 NUV-HD3 optical units have been successfully integrated on the pSCT camera, together with 64 HAMAMATSU MPPCs. An upgrade of the pSCT camera is foreseen over the next years when the full focal plane is expected to be equipped entirely with FBK NUV-HD3 SiPMs, for a total of 11328 pixels.