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The Probe for Luminosity Measurement detector is a novel luminometer designed to monitor the luminosity and beam conditions of the Large Hadron Collider at the interaction point of the LHCb experiment, starting from Run 3. The detector is based on a hodoscope composed of 48 Hamamatsu R760 photomultiplier tubes, which detect the Cherenkov light produced by charged particles originating from the interaction region. The accurate and stable operation of these sensors is essential to ensure reliable luminosity measurements throughout the full data-taking period. This paper presents a detailed characterisation of the photomultiplier tubes currently installed in the detector. In particular, their absolute gain, transit-time drift, linearity, dark current, and ageing behaviour are systematically studied under controlled laboratory conditions. The results provide a comprehensive assessment of the performance of the detection modules and establish the optimal operating conditions required to ensure stable and precise measurements throughout Run 3 and Run 4.