Correlated measurement of the lifetime and of the lineshape of the 511 keV annihilation radiation of positrons (age-momentum correlation, AMOC) has become a powerful tool for investigating reactions of positron or positronium in condensed matter as a function of time. The beam-based+ AMOC method installed at the Stuttgart relativistic positron beam facility (Ekine+4MeV) offers substantial advantages over the conventional E coincidence technique resulting in a fast data taking due to the unity detection efficiency of the+ scintillator which provides the start signal for the lifetime measurement. In this paper the application of AMOC to positronium chemistry is illustrated by the study of spin conversion of positronium in the system methanol/HTEMPO as a function of HTEMPO (4-hydroxy-2,2,6,6-tetramethylpiperidine-1-oxyl, a paramagnetic solute) concentration. The same technique can be applied to other systems and other reactions in positronium chemistry, e. g., oxidation or complex formation.