In this paper, we propose a novel network architecture for integrating terrestrial and non-terrestrial networks (NTNs) to establish connection between terrestrial ground stations which are unconnected due to blockage. We propose a new network framework where reconfigurable intelligent surface (RIS) is mounted on an aerodynamic high altitude platform station (HAPS), referred to as aerodynamic HAPS-RIS. This can be one of the promising candidates among non-terrestrial RIS (NT-RIS) platforms. We formulate a mathematical model of the cascade channel gain and time-varying effects based on the predictable mobility of the aerodynamic HAPS-RIS. We propose a multi-objective optimization problem for designing the RIS phase shifts to maximize the cascade channel gain while forcing the Doppler spread to zero, and minimizing the delay spread upper bound. Considering an RIS reference element, we find a closed-form solution to this optimization problem based on the Pareto optimality of the aforementioned objective functions. Finally, we evaluate and show the effective performance of our proposed closed-form solution through numerical simulations.