Facebook Messenger now offers Dropbox integration which allows users to send Pictures, Videos and Documents. The File sharing is possible without leaving Facebook Messenger. This service is accessible from the More Button in the Messenger (The Button is in right side of the conversion). Open Dropbox from there and Sign in to your Cloud Sharing Service. After Signing in you will be able to see your files right there.
While Sending Pictures or Videos, you will get Preview of the File. You have to Switch to Dropbox App for other Files. This Integration is Now Available for Android and iOS.