There are many benefits to claiming your Facebook email address:
It’s free and easy to set up.
Having your email integrated with your messages, chats and texts makes it easier to check them all at once. And if you’re looking for a message later, you don’t have to worry about how it was sent since all your different types of messages are in one place.
Your Facebook messages are compatible with traditional email systems (e.g., Hotmail, Yahoo or Gmail). When people send you emails from these external systems, they’re delivered directly to your Facebook Messages. And when you send messages to external email addresses, they’re formatted to look like your messages on Facebook, including your name and profile picture along with your message.
Owning your @facebook.com address makes it easier for friends and family who are not on Facebook yet to connect with you.
Your other email addresses may change over time, but your Facebook email never does.