Cotangent-bundle Fueter–Fukaya–Seidel conjecture

Let $L$ be an exact Kähler manifold, let $W$ be a holomorphic Morse function on $L$, and let $L'$ be the graph of $dW$ in $T^*L$. Cotangent-bundle Fueter–Fukaya–Seidel conjecture. The Hom-category $\operatorname{Hom}_{\mathrm{Ft}(T^*L)}(L,L')$ in the Fueter 2-category of $T^*L$ coincides with the Fukaya–Seidel category of $(L,W)$. This is the cotangent-bundle test case for the proposed Fueter 2-category; the source gives no resolution.