I left a passport onboard (with some cash, in a LV wallet). I had the concierge call the next station the FIN was due to arrive at. Through the telephone game, the SD confirmed the passport had been turned into a YVR gate agent already.
The concierge was very confident I'd recover my passport. I never saw it, or my wallet, or my cash again.
Of course there are times when AC has recovered items I left on the plane, I appreciate them for that.
Definitely a good idea to follow the suggestion above about contacting AC social media and listing the contents of said passport wallet to them for extra accountability.