  We present the complete supersymmetric and $\kappa$--symmetric action for the
4-dimensional interacting system of open supermembrane, dynamical supergravity
and 3--form matter multiplets. The cases of a single 3-form matter multiplet
and a quite generic model with a number of nonlinear interacting double 3-form
multiplets are considered. In all cases the fermionic parameter of the
$\kappa$-symmetry is subject to two apparently different projection conditions
which suggests that the ground state of the system, in particular a domain
junction, might preserve at most 1/4 of the spacetime supersymmetry. The
boundary term of the open supermembrane action, needed to preserve the
$\kappa$-symmetry, has the meaning of the action of a superstring. The
Wess--Zumino term of this superstring action is expressed in terms of real
linear superfield playing the role of St\"uckelberg field for the 3--form gauge
symmetry. This indicates that this symmetry is broken spontaneously by the
superstring at the boundary of supermembrane.
