  We show that the DC Josephson effect with ultracold fermionic gases in the
BEC regime of composite molecules can be described by a nonlinear Schrodinger
equation (NLSE). By comparing our results with Bogoliubov-de Gennes
calculations [Phys. Rev. Lett. 99, 040401 (2007)] we find that our superfluid
NLSE, which generalizes the Gross-Pitaevskii equation taking into account the
correct equation of state, is reliable in the BEC regime of the BCS-BEC
crossover up to the limit of very large (positive) scattering length. We also
predict that the Josephson current displays relevant beyond mean-field effects.
