  We derive boundary conditions for the coupled spin-charge diffusion equations
at a transmitting interface between two-dimensional electron systems with
different strengths of the Rashba spin-orbit (SO) coupling $\alpha$, and an
electric field parallel to the interface. We consider the limit where the
spin-diffusion length l_s is long compared to the electron mean free path l,
and assume that $\alpha$ changes discontinuously on the scale of l_s. We find
that the spin density is also discontinuous on the scale of l_s. In the case
where the electron mobility is constant across the interface, this leads to the
complete suppression of the expected spin injection from a region with
$\alpha\neq0$ into a non-SO region with $\alpha=0$.
