I can only find info on how to go from Facebook to Gravatar but not the other way. Maybe I'm the only fool that would want to do this? :-)
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To copy this change to all your Stack Exchange accounts, try clicking "Save and Copy Profile to all Stack Exchange Accounts" at the bottom of the "Edit Profile" page on http://facebook.stackoverflow.com
The avatar shown in Stack Exchange site is the one you have on gravatar.com, if there is one that matches the email address you have associated with your account. There isn't an option that allows you to decide which avatar you want to use on your Stack Exchange account.
If you log in to facebook.stackoverflow.com using Facebook, facebook.stackoverflow.com and Stack Overflow will use the picture set in your Facebook profile.
The other method is to create another gravatar from your Facebook picture, and associate it with an email address that you use in your Stack Exchange accounts. As some email providers allow you to use email addresses such as email@example.com, which will send the messages to firstname.lastname@example.org, you can associate the new gravatar to a similar addy, and you would get email from Stack Exchange at the usual email address.