  We examine transfer of particle entanglement and spin squeezing between
atomic and photonic subsystems in optical cavities coupled by two-photon
exchange. Each cavity contains a single atom, interacting with cavity photons
with a two-photon cascade transition. Particle entanglement is characterized by
evaluating optimal spin squeezing inequalities, for the cases of initially
separable and entangled two-photon states. It is found that particle
entanglement is first generated among the photons in separate cavities and then
transferred to the atoms. The underlying mechanism is recognized as an
inter-cavity two-axis twisting spin squeezing interaction, induced by
two-photon exchange, and its optimal combination with the intra-cavity
atom-photon coupling. Relative effect of non-local two-photon exchange and
local atom-photon interactions of cavity photons on the spin squeezing and
entanglement transfer is pointed out.
