Next generation wireless communication networks intend to take advantage of the integration of terrestrial and aerospace infrastructures. Besides, multiple-input multiple-output (MIMO) architecture is the key technology, which has brought the wireless gigabit vision closer to reality. In this direction, high-altitude platforms (HAPs) could act as relay stations in the stratosphere transferring information from an uplink to a downlink MIMO channel. This paper investigates the performance of a novel transmission scheme for the delivery of mobile-to-mobile (M-to-M) services via a stratospheric relay. It is assumed that the source, relay, and destination nodes are equipped with multiple antennas and that amplify-and-forward (AF) relaying is adopted. The performance is analyzed through rigorous simulations in terms of the bit-error rate (BER) by using a recently proposed 3D geometry-based reference model in spatially correlated flat-fading MIMO channels, employing a hierarchical broadcast technique and minimum mean square error (MMSE) receivers.