The dependence of the angular momentum polarization (orientation and alignment) of the fragments on the direction of ejection k, is studied quantum mechanically for molecular photodissociation into two fragments of which one carries an angular momentum j. Explicit expressions in terms of the transition matrix elements for electronic excitation into the final dissociative states are given in the axial-recoil limit and for different photon polarizations. The importance of interference effects due to coherent excitation of dissociative states with different helicity quantum numbers (the projection Omega of j on the recoil direction k) is stressed. It is shown that not only absolute magnitudes but also relative phases of individual transition matrix elements can be determined separately if the spatial anisotropy of the angular momentum polarization is measured.