  We study the local theta correspondence for dual pairs of the form
$\mathrm{Aut}(C)\times F_{4}$ over a $p$-adic field, where $C$ is a composition
algebra of dimension 2 or 4, by restricting the minimal representation of a
group of type $E$. We investigate this restriction through the computation of
maximal parabolic Jacquet modules and the Fourier-Jacobi functor.
  As a consequence of our results we prove a multiplicity one result for the
$\mathrm{Spin}(9)$-invariant linear functionals of irreducible representations
of $F_{4}$ and classify the $\mathrm{Spin}(9)$-distinguished representations.
