Sooty mold on birch

[STOVE]

My neighbor has a big birch in his backyard that seems to have a sooty mold issue. He has asked me what I think and I told him I was unsure of what to do. He doesn’t want to lose the tree and its shade

Leave it be?
Remove the trunk with the mold?

 

[ATH]

Not great pics ...

IF it's sooty mold, that likely means something is there excreting honeydew. You need to figure out what that is.