I sent the completed Princess Shareholder Benefit form as well as a copy of my most recent (August) brokerage statement to sbpcl@princesscruises.com last Monday, September 18th and had the credit added to my account on Thursday, September 21st. So, if they have all the required info, it should be super quick.
I never received a notification email, I just happened to be on my account to look at something else when I saw it had been added.