Air currents can carry bacteria and mold spores into stratospheric altitudes. Early balloon collections found bacteria and mold in air samples at a little above 71 thousand feet altitude. There were only a few colonies, but we also know that our bacterial media often do not allow many microorganisms to grow.
More recent studies of the atmospheric microbiome have indicated that a wide variety of bacteria and fungi can routinely be found in the atmosphere thousands of feet up. Modern measurements find about 10 million living microbes per cubic meter.
Sandstorms or jet streams are known to be able to move living bacteria long distances. Spores are often of about the same size and I see no reason why we will not find that they do the same.