do it. gills side down. maybe score the stump a with like a few fresh nicks/cuts so water might pool in little pockets. do that to part of the outer/bark layer too, so a few nicks/cuts cross the heartwood/outer boundary.

and maybe even leave the material resting on part of it. that way you're hitting all the permutations of inoculation environment (shady, aerobic, waterphilic, anaerobic, full sun, and all the available wood structures.

I have my doubts it'll do anything, but for like 30 seconds of chill/amusing effort to accelerate a stump's decay, the reward is high. stump removal is such a pain in the ass.

also, you can't go wrong making allies with random endemic fungi! #TeamCordyceps

Proof so nobody calls me a fake

go over and ask if you can have it

Update, ive liberated the mushroom

Looks like a lawn. While some would be sad to have a mushroom taken, this one is likely to be annihilated. Without knowing what kind of shroom may not be a good idea. Getting some spores for edible mushrooms to seed the stump may be better, iirc substrate is often sterilised first though so look into it first.