  We investigate the behavior of a Josephson junction consisting of a
ferromagnetic insulator-superconductor (FI-S) bilayer tunnel-coupled to a
superconducting electrode. We show that the Josephson coupling in the structure
is strenghtened by the presence of the spin-splitting field induced in the FI-S
bilayer. Such strenghtening manifests itself as an increase of the critical
current $I_c$ with the amplitude of the exchange field. Furthermore, the effect
can be strongly enhanced if the junction is taken out of equilibrium by a
temperature bias. We propose a realistic setup to assess experimentally the
magnitude of the induced exchange field, and predict a drastic deviation of the
$I_c(T)$ curve ($T$ is the temperature) with respect to equilibrium.
