Antihydrogen is at the focus of antimatter research. One of the main aims is to perform a direct test of the fundamental CPT symmetry by comparing the spectroscopic properties of the ground-state antihydrogen atom with those of the hydrogen atom. In current experiments synthetized antihydrogen is formed mainly via the three-body recombination process after mixing positron and antiproton clouds together in a cryogenic trap. The major three-body formation process populates mainly highly excited Rydberg states, therefore before the antihydrogen atoms reach the ground-state additional processes may take place, such as collisional (de)excitation, ionization and spontaneous or stimulated radiative transitions. We have used a classical-trajectory Monte Carlo (CTMC) code along with regular atomic codes to generate a scattering database of rate coefficients in various experimentally achievable magnetic field strengths and in low temperature positron plasma conditions. We used these rates to calculate the evolution of level population of antihydrogen during formation, scattering and flight within our experimental conditions [1]. The model and the results are presented.