  We propose an experimental procedure to find out the medium modifications of
the $\phi$ meson. The reaction is inclusive $\phi$ photoproduction in nuclei,
looking for $K^+ K^-$ pairs from the $\phi$ decay with total momentum smaller
than 100-150 $MeV/c$, which are made possible at energies of present
laboratories from center of mass $\phi$ backward production and the help of
Fermi motion. We have conducted a many body calculation of the mass
distribution of the $\phi$ adapted to the experimental set up of a recent JLAB
experiment where the backwards $\phi$ photoproduction has been measured. Using
recent results for the in medium properties of the $\phi$, we find that the
width of the invariant mass distribution for photoproduction on medium to heavy
nuclei is larger than the free $\phi$ width by a factor of two or more.
