I found a lot of information about forwarding email from other accounts to Facebook. But I could not find anything about going the other way. I want to forward email from my @facebook address to Gmail.
It’s not exactly a forward per se, but you can use the notifications feature to receive the messages to your email address associated with your Facebook account—not the
@facebook.com one, but the
@at_your_email_provider.com one—which needs to be set as the primary email address. The problem is that it doesn’t discriminate between emails sent to
@facebook.com and Facebook messages, it forwards everything. Also note that it’s not really reliable, sometimes the messages being delivered and sometimes not.