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Asymptotic giant branch (AGB) stars are thought to be among the most important sources of fluorine in our Galaxy. While observations and theory agree at close-to-solar metallicity, stellar models overestimate fluorine production in comparison to heavy elements at lower metallicities. We present predictions for 19F abundance for a set of AGB models with various masses and metallicities, in which magnetic buoyancy induces the formation of the 13C neutron source (the so-called 13C pocket). In our new models, fluorine is mostly created as a consequence of secondary 14N nucleosynthesis during convective thermal pulses, with a minor contribution from the 14N existing in the 13C pocket zone. As a result, AGB stellar models with magnetic-buoyancyinduced mixing show low 19F surface abundances which agree with fluorine spectroscopic observations at both low and near-solar metallicity.