PHased Arrays for Reflector Observing Systems (PHAROS) is a C-band (4-8GHz) Phased Array Feed (PAF) receiver designed to operate from the primary focus of a large single-dish radio astronomy antenna. It consists of an array of 220-element Vivaldi antennas (10×11×2 polarization), cryogenically cooled at roughly 20K along with low noise amplifiers (LNAs), and of analogue beamformers cryogenically cooled at roughly 80K. PHAROS2, the upgrade of PHAROS, is a PAF demonstrator developed in the framework of the Square Kilometer Array Advanced Instrumentation Program (SKA AIP) with the goal of investigating the potential of the PAF technologies at high frequencies in view of their possible application on the SKA dish telescopes. The PHAROS2 design includes new cryogenically cooled LNAs with state-of-the-art performance, a digital beamformer capable of synthesizing four beams from a sub-array of 24 single-polarization antenna elements, and a C-band multi-channel Warm Section receiver capable of analogue filtering and down-converting the signals from the antennas to a suitable frequency range at the input of the digital backend, providing an instantaneous bandwidth of 275MHz for each signal. In this paper, we describe the design and performance of the PHAROS2 digital backend/beamformer, based on the Italian Tile Processing Module (ITPM) hardware, which was initially developed for the SKA Low Frequency Aperture Array (LFAA). The backend was adapted to perform the beamforming for our PAF application. We describe the implementation of the beamformer on the Field Programmable Gate Arrays (FPGAs) of the ITPM and how the backend was successfully used to synthesize four independent beams, both in the laboratory (across the entire 275MHz instantaneous bandwidth) and during on-field observations at the BEST-2 array (across 16MHz instantaneous bandwidth), which is a subset of the Northern Cross Radio Telescope (located in the district of Bologna, Italy). The beamformer design allows re-scaling to a greater number of beams and wider bandwidths.