It is shown experimentally that the rate of the 3-photon annihilation of positrons in amorphous insulators exhibiting a long-lifetime component in 2-photon decay (Teflon, fused quartz) is quenched in the presence of an external magnetic field, while the rate in aluminum in unaffected. This effect has been studied in fields up to 104 gauss. The results can tentatively be explained by a simple theory which assumes: (a) that in metals, all or most positrons do not form bound systems; (b) in amorphous insulators a certain fraction of positrons form 1S positronium, the rest annihilating directly; (c) in amorphous insulators such as Teflon and fused quartz, positronium atoms, or at least their ortho-variety, exhibit essentially vacuum intrinsic properties and are subject to a rapid destruction due to ortho <--> para conversion and/or "pickoff" annihilation. Besides the (vacuum) ortho and para annihilation rates, the sole parameter of this theory is the "conversion" rate γ. The values of γ determined from the present experiment agree within 10% with those required to explain the lifetimes observed in these materials by Bell and Graham. Accurate relative 3-photon annihilation rates have also been obtained: (Teflon/Al)=3.08+/-0.15 (fused quartz/Al)=2.29+/-0.09.