In this work, the performance analysis of a dual-hop relay transmission system composed of asymmetric radio-frequency (RF) and unified free-space optical (FSO) links subject to pointing errors is presented. These unified FSO links account for both types of detection techniques (i.e. indirect modulation/direct detection (IM/DD) as well as heterodyne detection). More specifically, we derive new exact closed-form expressions for the cumulative distribution function, probability density function, moment generating function, and moments of the end-to-end signal-to-noise ratio of these systems in terms of the Meijer's G function. We then capitalize on these results to offer new exact closed-form expressions for the outage probability, higher-order amount of fading, average error rate for binary and M-ary modulation schemes, and ergodic capacity, all in terms of Meijer's G functions. All our new analytical results are verified via computer-based Monte-Carlo simulations.