  We classify the simple restricted modules for the minimal $p$-envelope of the
non-graded, non-restricted Hamiltonian Lie algebra $H(2; (1,1); \Phi(1))$ over
an algebraically closed field $k$ of characteristic $p \geq 5$. We also give
the restrictions of these modules to a subalgebra isomorphic to the first Witt
Algebra, a result stated in [S. Herpel and D. Stewart, \emph{Selecta
Mathematica} 22:2 (2016) 765--799] with an incomplete proof.
