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Infrared free-space optics (FSO) provide an attractive solution for ultra-high-capacity wireless communications. However, the full potential of FSO is still being hindered by the apparent random fluctuations on the received optical power, which can be triggered by external factors such as atmospheric turbulence, weather instability, and pointing errors. Through the analysis of long-term experimental measurements, we identify the existence of significant time-domain memory in outdoor FSO links, which is found to be particularly strong under rainy weather conditions. Following this observation, we demonstrate that these memory effects can be effectively utilized to design accurate FSO channel estimation algorithms. Taking advantage of the arbitrary bit-rate granularity provided by probabilistic constellation shaping (PCS), and resorting to a simple moving average channel estimator, we demonstrate 400G+ transmission …