We analyze the outage probability of integrated ground-air-space free-space optical (FSO) communication links for different atmospheric turbulence channel models. The performance of ground to high altitude platforms (HAPS), HAPS to geostationay Earth orbit (GEO) satellite, HAPS to HAPS and ground to GEO satellite is investigated for various link configurations (downlink, horizontal, and uplink) and parameters such as zenith angle, channel state, horizontal and vertical deviations, altitude, beam waist, receiver aperture diameter, wind speed, and visibility. The atmospheric attenuation (the effects of fog, cloud and volcanic activities), atmospheric turbulence, angle of arrival (AOA) fluctuations and pointing error are included in the considered model. Closed-form expressions for the probability density function (PDF) and cumulative distribution function (CDF) are obtained for Lognormal, Gamma and exponentiated Weibull distributed channel models. The benefit of using HAPS is shown by comparison of outage probabilities for direct ground to GEO satellite and HAPS assisted ground to GEO satellite links.