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This paper aims to describe the Pointing Reconstruction Model (PRM) and the prototype Star Tracker, which will be mounted on LSPE-Strip, a microwave Q- and W-band CMB telescope planned for installation at the "Observatorio del Teide" in Tenerife. The PRM integrates information on the instantaneous attitude provided by the telescope control system to determine the actual pointing direction and focal plane orientation of the telescope. It accounts for various non-idealities in the telescope setup, represented by eight configuration angles, which will be calibrated using the Star Tracker. Following the derivation of the PRM formalism and its implementation, we investigate the pointing errors caused by incorrect calibration of these configuration angles to validate the required 1 arcminute maximum systematic pointing error for the LSPE-Strip survey. This paper also describes the main structure and operations of the Star Tracker and presents the results of a campaign of actual sky observations conducted with a prototype. The results demonstrate a Star Tracker RMS accuracy of approximately 3 arcseconds, while systematic errors remain below 10 arcseconds. Based on these results, we analyzed the problem of reconstructing the PRM configuration angles. Two methods for intercalibrating the Star Tracker's pointing direction with respect to the focal plane's pointing direction were examined: (1) observations of planets and (2) observations of a drone carrying both an optical beacon and a radio beacon. In the first case, an intercalibration accuracy between 1/3 arcminute and 1 arcminute is achievable. In the second case, the expected intercalibration accuracy ranges from 0.25 arcminute to 1 arcminute., Comment: 37 pages; 16 figures; 5 tables; the limited length of the arXiv abstract required shortening the original abstract, which is presented in its full length in the PDF; paper accepted for pubblication 2025 jan 06 in the Journal of Instrumentation (JINST)