In this work we construct for a given smooth, generic Hamiltonian $H : mathbb{S}^1timesmathbb{T}^n longrightarrow mathbb{R}$ on the torus a chain isomorphism $ Phi_* : big(C_*(H),partial^M_*big) longrightarrow big(C_*(H),partial^F_*big)$ between the
Morse complex of the Hamiltonian action $A_H$ on the free loop space of the torus $Lambda_0(mathbb{T}^n)$ and the Floer complex. Though both complexes are generated by the critical points of $A_H$, their boundary operators differ. Therefore the construction of $Phi$ 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.
