  We consider a scalar conservation law with a spatially discontinuous flux at
a single point $x=0$, and we study the initial data identification problem for
$AB$-entropy solutions associated to an interface connection $(A,B)$. This
problem consists in identifying the set of initial data driven by the
corresponding $AB$-entropy solution to a given target profile~$\omega^T$, at a
time horizon $T>0$. We provide a full characterization of such a set in terms
of suitable integral inequalities, and we establish structural and geometrical
properties of this set. A distinctive feature of the initial set is that it is
in general not convex, differently from the case of conservation laws with
convex flux independent on the space variable. The results rely on the
properties of the $AB$-backward-forward evolution operator introduced
in~\cite{talamini_ancona_attset}, and on a proper concept of
$AB$-genuine/interface characteristic for $AB$-entropy solutions provided in
this paper.
