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Whenever you transfer the player to another map using the built-in event command, Essentials automatically cancels all vehicles. However, Essentials has a script method Kernel.pbTransferUnderwater that you can probably call from a script command in the doorway's event rather than using the Transfer Player command.
Take the mapid, x, and y from your current transfer command and put it in that script in your door's event, and remove the Transfer command you have in there already. See if that works.
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If that doesn't work for some reason, you may want to try the following script placed in an "autorun-once" event on the underwater cave map (that is, an autorun event on the map that checks for tsIsOff?("A")):