Answer: A green fungus is probably lichen, which is harmless and grows where there is high humidity and poor air circulation. Lots of trees and shrubs develop lichen growth and it eventually sloughs off on its own. Lack of leaves is a concern, though. Too much shade can cause it (the the lichen, too). If you can't remove the limbs of other trees to allow more sunlight, you can try pruning your tree back to encourage new growth and try watering deeply once a week during the growing season. Shade and dry soils will keep your tree from leafing out as it should. Hope this helps!
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