  Currently, the structure of the $X(3872)$ meson is unknown. Different
competing models of the $c\bar c$ exotic state $X(3872)$ exist, including the
possibilities that this state is either a mesonic molecule with dominating $D^0
\bar D^{*0} +c.c.$ composition, a $c \bar c q \bar q$ tetraquark, or a $c \bar
c$-gluon hybrid state. It is expected that the $X(3872)$ state is rather
strongly coupled to the $\bar p p$ channel and, therefore, can be produced in
$\bar p p$ and $\bar pA$ collisions at PANDA. We propose to test the
hypothetical molecular structure of $X(3872)$ by studying the $D$ or $\bar
D^{*}$ stripping reactions on a nuclear residue.
