In this work, for a given smooth, generic Hamiltonian $${H : \mathbb{S}^{1} \times \mathbb{T}^{2n} \rightarrow \mathbb{R}}$$ H : S 1 × T 2 n → R on the torus $${\mathbb{T}^{2n} = \mathbb{R}^{2n}/\mathbb{Z}^{2n}}$$ T 2 n = R 2 n / Z 2 n we construct a chain isomorphism $${\Phi_{*} : (C_{*}(H), \partial^{M}_{*}) \rightarrow (C_{*}(H), \partial^{F}_{*})}$$ Φ ∗ : ( C ∗ ( H ) , ∂ ∗ M ) → ( C ∗ ( H ) , ∂ ∗ F ) between the Morse complex of the Hamiltonian action AH on the free loop space of the torus $${\Lambda_{0}(\mathbb{T}^{2n})}$$ Λ 0 ( T 2 n ) and the Floer complex. Though both complexes are generated by the critical points of A H , their boundary operators differ. Therefore, the construction of $${\Phi}$$ Φ is based on counting the moduli spaces of hybrid-type solutions which involves stating a new non-Lagrangian boundary value problem for Cauchy–Riemann type operators not yet studied in Floer theory. We finally want to note that the problem is completely symmetric. So we also could construct an isomorphism $${\Psi_{*} : (C_{*}(H), \partial^{F}_{*}) \rightarrow (C_{*}(H), \partial^{M}_{*})}$$ Ψ ∗ : ( C ∗ ( H ) , ∂ ∗ F ) → ( C ∗ ( H ) , ∂ ∗ M ) .