  This is a sequel to our paper arXiv:2008.13462, where we proposed a
definition of the Morse homotopy of the moment polytope of toric manifolds.
Using this as the substitute of the Fukaya category of the toric manifolds, we
proved a version of homological mirror symmetry for the projective spaces and
their products via Strominger-Yau-Zaslow construction of the mirror dual
Landau-Ginzburg model. In this paper we go this way further and extend our
previous result to the case of the Hirzebruch surface $\mathbb{F}_1$.
