  We construct a full rectangular Lefschetz collection in the derived category
of the adjoint Grassmannian in type $\mathrm{F}_4$. This gives the first
example of a full exceptional collection on this variety and also completes the
proof of a conjecture due to Alexander Kuznetsov and the author that relates
the structure of the derived category of coherent sheaves to the small quantum
cohomology in the case of adjoint varieties for non-simply laced groups.
