Positrons injected in molecular solids or polymers will have positronium formation around the terminal spur of the positron track, the so-called positron spur, with active species in the spur, such as excess electrons. In the usual case, the electrons are not polarized. At low enough temperatures, long-lived weakly localized electrons are accumulated by irradiation in darkness, and positrons will have a chance to form positronium with these long-lived weakly localized electrons. For these electrons, it is possible to cause them to be polarized by applying a magnetic field at very low temperatures. We have successfully observed the effect on the positronium formation reaction of polarized positrons and polarized electrons.