  Motivated by a recent experiment evidencing triplet superconductivity in a
ferromagnetic Josephson junction with a Cu$_2$MnAl-Heusler barrier, we
construct a theoretical model accounting for this observation. The key
ingredients in our model which generate the triplet supercurrent are
\textit{spin-active zones}, characterised by an effective canted interface
magnetic moment. Using a numerical solution of the quasiclassical equations of
superconductivity with spin-active boundary conditions, we find qualitatively
very good agreement with the experimentally observed supercurrent. Further
experimental implications of the spin-active zones are discussed.
