The fungus spreads to new locations using resistant spores. These can be either sexual or asexual (cloning). They usually spread by wind, but some species rely on animals to be moved around.
Sources
Sciencelearn – Fungal life cycles – spores and more 
Britannican – Study the different ways mushrooms release spores
April 2023, TÄNKOM | Revised March 2024 RETHINK
