  Subdiffusion with reaction $A+B\rightarrow B$ is considered in a system which
consists of two homogeneous media joined together; the $A$ particles are mobile
whereas $B$ are static. Subdiffusion and reaction parameters, which are assumed
to be independent of time and space variable, can be different in both media.
Particles $A$ move freely across the border between the media. In each part of
the system the process is described by the subdiffusion--reaction equations
with fractional time derivative. By means of the method presented in this paper
we derive both the fundamental solutions (the Green's functions) $P(x,t)$ to
the subdiffusion--reaction equations and the boundary conditions at the border
between the media. One of the conditions demands the continuity of a flux and
the other one contains the Riemann--Liouville fractional time derivatives
$\partial^{\alpha_1}P(0^+,t)/\partial
t^{\alpha_1}=(D_1/D_2)\partial^{\alpha_2}P(0^-,t)/\partial t^{\alpha_2}$, where
the subdiffusion parameters $\alpha_1$, $D_1$ and $\alpha_2$, $D_2$ are defined
in the regions $x<0$ and $x>0$, respectively.
