Here we study the XXZ spin chain under the boundary strong-coupling to non-markovian baths which we model as additional spin chains . The bath spin chains essentially work as a magnetization battery that drive the spin transport through the system. More specifically we prepare one terminal of the battery in the fully up-magnetized state |11...111⟩ while the other in the down-magnetized state |00...000⟩. The global initial state is of the from |ΨS⟩=|11...111⟩|S⟩|00...000⟩, with |S⟩ being an arbitrary system state. The system itself is prepared in a demagnetized state taken and we focus most of the manuscript on the case |S⟩=|G⟩, with G labelling the ground state of the Hamiltonian. This initial configuration |ΨG⟩ induces a strongly nonlinear transport response resembling the maximal bias regime in . Lower magnetization differences between the terminals of the battery eventually lead to the linear response regime at low bias . As opposed to the Markovian open system setting , we remark that the system-battery coupling we have suggested, in general, does not map to a simple phenomenological master equation. Deriving a closed form master equation for strongly interacting systems requires, in principle, the knowledge of the full eigen-decomposition of the system Hamiltonian , thus a hopeless task for a many-body problem. Therefore, addressing the full system plus bath Hamiltonian dynamics seems most appropriate in order to capture the strong coupling regime. Furthermore, the battery bears memory on the system initial state . As an alternative we prepare the system in the GHZ state $|GHZ\rangle=(|11...111\rangle+|00...000\rangle)/$ which has macroscopic similarities to the ground state preparation such as magnetization zero, however it is orthogonal to the ground state preparation. Interestingly, this initial state |ΨGHZ⟩ leads to different dynamical signatures providing an example of how microscopic details and non-Markovianity may affect the emergent phenomena.