Connect with Facebook with different emails
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I'm using Facebook Connect in my website. However, since it is optional, users can register via conventional signup form as well.

Now, when they want to post something, there will be a checkbox to Post to Facebook, but for it to appear, they must connect with Facebook first.

The problem is, say my Facebook account is henson_fb@gmail.com, however I registered on this site with my other email let's say henson@gmail.com. Logged in as henson@gmail.com, when I click Connect with Facebook in my site, the usual Facebook login and allow permission works, but the login part doesn't work, I figure because I check the user's email when they Connect to Facebook to know whether they are registered or not. 

So, is it possible to connect with Facebook in the scenario above?

Thanks.