The influence of 3 MW Hywind-II wind turbine wakes from an upstream offshore floating wind turbine on a downstream turbine with a separation distance of seven rotor diameters was studied for a site in the Gulf of Maine. The turbines and the platforms were subjected to atmospheric boundary layer flows. Various sensitivity studies on fatigue loads with respect to the positions of the downstream turbine were performed and validated with a large-eddy simulation tool. In particular, the effect of various lateral positions of the downstream turbine relative to the upstream turbine were considered using time-series turbine wake data generated from the large-eddy simulation tool which served as an input to an aero-elastic wind turbine model to assess the loads. The load response from the rotor, tower, and the floating platform for the downstream turbine were sensitive to the lateral offset positions where turbines that were partially exposed to upstream turbine wakes yielded significant increases in the cyclic load range. For the given set of lateral positions for the downstream turbine, the largest damage equivalent load occurred when the turbine was one rotor diameter to the left of the centerline, when looking upstream, which is the position of the turbine fully exposed to upstream turbine wake. On the other hand, the fatigue load on the downstream turbine placed on the right side of the position fully exposed to the upstream turbine wake, yielded lower stress due to the non-symmetric shape of the turbine wake. The configuration associated with the largest damage equivalent loads was further investigated in a large-eddy simulation, modeling both the upstream and downstream turbines. It was found that the energy spectra at the blade rotational frequency were a magnitude order higher for the downstream turbine, especially for surge, heave, pitch, and yaw motion of the platform. The increase of the damage equivalent load for the flapwise blade root moment was 45% compared to the upstream turbine, which can potentially reduce the turbine service life time.