  In this work we construct for a given smooth, generic Hamiltonian $H :
\mathbb{S}^1\times\mathbb{T}^n \longrightarrow \mathbb{R}$ 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.
