If you want that FB sends or discontinues sending your phone notifications, like when you get a text to your phone, go in to the FB app that is synced to your phone, press menu on your phone (bottom, far-left with three lines), then settings. From there you'll see the "Notifications" checkbox. Just check it to green to get notifications, or uncheck to discontinue notifications. Not quite sure if this is your problem, but I hope it helps!
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