Issues with tracking, precision pointing, and Doppler shift are the major sources of performance loss in laser inter-satellite communication that can severely decrease the coverage and overall performance of satellite constellations. As a solution to these problems, we propose a cooperation strategy in which a high altitude platform station (HAPS) staying at a quasi-stationary position contributes to the inter-satellite connectivity. In this setup, the HAPS node uses two different scheduling approaches: one that relies on the zenith angle; the other on instantaneous signal-to-noise ratio. To quantify the performance of the proposed scheme, overall outage probabilities for the two scheduling methods are obtained. In addition, guidelines for the design of practical inter-satellite networks are provided.