  We analyze the GeV gamma-ray emission data from the vicinity of the supernova
remnant (SNR) HB9 (G160.9+2.6) from the \textit{Fermi}-LAT 12-year observations
to quantify the evolution of diffusive shock acceleration (DSA) in the SNR. In
the vicinity of HB9, there are molecular clouds whose locations do not coincide
with the SNR shell in the line of sight. We detect significant gamma-ray
emissions above 1~GeV spatially coinciding with the two prominent cloud
regions, as well as a emission from the SNR shell, the latter of which is
consistent with the results of previous studies. The energy spectrum above
1~GeV in each region is fitted with a simple power-law function of $dN/dE
\propto E^{-\Gamma}$. The fitting result indicates harder spectra with
power-law indices of $\Gamma$ = $1.84 \pm 0.18$ and $1.84 \pm 0.14$ than that
at the SNR shell with $\Gamma$= $2.55 \pm 0.10$. The observed spectra from the
cloud regions are found to be consistent with the theoretically expected
gamma-ray emissions originating in the protons that escaped from SNR HB9, where
particles can be accelerated up to higher energies than those at the shell at
present. The resultant diffusion coefficient in the vicinity of the SNR is
comparable to that of the Galactic mean.
