Nucleosynthesis of fluorine in the context of helium burning occurs through the N-15(alpha, gamma)F-19 reaction. At temperatures where fluorine formation takes place in most astrophysical models, the narrow resonance associated with the 4.378 MeV level of F-19 is expected to dominate the reaction rate, but its strength is not known. We used a N-15 confined gas target to study this level by means of the transfer reaction N-15(Li-7,t) F-19 at 28 MeV. Reaction products were analysed with a split pole magnetic spectrometer and the angular distributions for the first 16 levels of F-19 were extracted, These distributions are fairly well reproduced by FR-DWBA calculations in the framework of an alpha-cluster transfer model with a compound-nucleus contribution obtained by Hauser-Feshbach calculations. alpha-spectroscopic factors were deduced and, for unbound levels, the alpha-widths were determined and compared with the existing direct measurements, The alpha-width of the level of astrophysical interest (E(x) = 4.378 MeV) was found to be Gamma(alpha) = 1.5 x 10(-9) eV, a value 60 times smaller than the commonly used one. The astrophysical consequences for F-19 production in AGE stars are discussed.