How would you know if your history was approved?
Very specifically, if you type in @history, the very first line of an approved character history will read...
"You have an approved history. Type 'help employment' for more info on getting a job!"
If you are logged in when your history is approved, you'll get a one lined notification of it. I think it also happens if it is declined and you need to try again. There is no additional notification that occurs if you are logged out when it happens, to my knowledge, so you can and probably should check @history when you log in to see if you are good to go or if you need to make corrections.