It will be fine leaving in there. It's (sintered) stainless steel, as inert as your SS conical.
Once the beer has transferred and you retrieved it, you need to give the inside a good thorough cleaning. That's a more laborious job. You need to get the beer out of the pores.
For that I've pushed Starsan through the stone, repeatedly. Then left it submerged in Starsan for a day, and pushed it out again. Repeat x times until you're satisfied it's clean.
How did the stone pop off?