  This paper presents a detailed characterization of the positron beam
delivered by the Beam Test Facility at Laboratori Nazionali of Frascati to the
PADME experiment during Run III, which took place from October to December
2022. It showcases the methodology used to measure the main beam parameters
such as the position in space, the absolute momentum scale, the beam energy
spread, and its intensity through a combination of data analysis and Monte
Carlo simulations. The results achieved include an absolute precision in the
momentum of the beam to within $\sim$ 1-2 MeV$/c$, a relative beam energy
spread below 0.25\%, and an absolute precision in the intensity of the beam at
the level of 2\% percent.
