As far as I know, and someone s,arter than me may know different, there is no way of doing this from the phone natively.
But, there is a workaround...you must do it from the full FaceBook website...no the FaceBook app or Social Widget...
Open a web browser and navigate to FaceBook and log in.
Now just click the Video Button and then select the Upload from Computer Button.
This will make the phone ask where to look for the file...choose where the video is and then select the video.
The video file has to be less than 1024MB in size ad under 20 minutes in duration...
I just tested this method and know it works...good luck!