Point-spread function (PSF) reconstruction (PSF-R) is a well-established technique to determine the PSF reliably and accurately from adaptive optics (AO) control-loop data. We have successfully applied this technique to improve the precision of photometry and astrometry for observations of NGC 6121 obtained with the Spectro Polarimetric High-contrast Exoplanet REsearch (SPHERE)/Zurich Waging POLarimeter (ZIMPOL), which will be presented in a forthcoming Letter. First, we present the methodology we followed to reconstruct the PSF by combining pupil-plane and focal-plane measurements using our PSF-R method PRIME (PSF Reconstruction and Identification for Multiple-source characterization Enhancement), with upgrades of both the model and best-fitting steps compared with previous articles. Secondly, we highlight that PRIME allows us to maintain the PSF fitting residual below 0.2 percent over 2 hours of observation and using only 30 s of AO telemetry, which may have important consequences for telemetry storage for PSF-R purposes on future 30-40 m class telescopes. Finally, we deploy PRIME in a more realistic regime using faint stars, so as to identify the precision needed on the initial-guess parameters to ensure convergence towards the optimal solution.