  We study the Josephson effect in a triplet
superconductor--ferromagnet--singlet superconductor junction. We show that the
interaction of tunneling Cooper pairs with the interface magnetization can
permit a Josephson current at the lowest order of a tunneling Hamiltonian
perturbation theory. Two conditions must be satisfied for this to occur: the
magnetization of the ferromagnet has a component parallel to the ${\bf
d}$-vector of the triplet superconductor, and the gaps of the superconductors
have the same parity with respect to the interface momentum. The resulting
charge current displays an unconventional dependence on the orientation of the
magnetic moment and the phase difference. This is accompanied by a
phase-dependent spin current in the triplet superconductor, while a
phase-independent spin current is always present. The tunneling perturbation
theory predictions are confirmed using a numerical Green's function method. An
analytical treatment of a one-dimensional junction demonstrates that our
conclusions are robust far away from the tunneling regime, and reveals
signatures of the unconventional Josephson effect in the critical currents.
