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Facebook's email notifications are usually just annoying, and when we often recommend turning them off. Weblog MakeUseOf dicsovers a good reason to keep them on: it makes your entire Facebook archive searchable.
All you need to do is turn on Facebook's email notifications, then set up a Gmail filter that automatically marks them as read, archives them and labels them. That way, you never have to deal with them cluttering up your inbox for a direct link.
Here is a step by step guide.