The transfer of orbital angular momentum from vortex beams to optically induced photonic lattices is demonstrated. It is found that the sum of the angular momenta of interacting incoherent counterpropagating (CP) beams is not conserved, whereas their difference is. The sum of angular momenta of copropagating (CO) interacting beams is strictly conserved. It is also found that the transfer of angular momentum in CP interacting beams is minimal, amounting to a few percent, whereas the transfer in CO interacting beams is substantial, amounting to tens of percent. In fixed lattices, for both CP and CO beams, angular momentum is never conserved.
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