  The present day experimental data on the $X(3872)$ decays do not allow to
make clear conclusions on the dominating structure of this state. We discuss
here an alternative way to study its structure by means of the two-step $\bar
D^*$ (or $D$) production in $\bar p A$ reactions. If this process is mediated
by $X(3872)$, the characteristic narrow peaks of the $\bar D^*$ (or $D$)
distributions in the light cone momentum fraction at small transverse momenta
will appear. This would unambiguously signal the $D \bar D^*$ + c.c. molecular
composition of the $X(3872)$ state.
