That would not solve your problem either. I could be using a different email for youtube and facebook. Check for some APIs for youtube and facebook that lets the current user do things.
Edit: Here are some links, if we assume that you want to help users upload videos they've uploaded to Facebook to their YouTube accuont.
You can access all the videos uploaded by this URL https://graph.facebook.com/me/videos/uploaded?access_token=YOUR_TOKEN
which will give you a list of Videos
(found this information at the facebook API reference)
Then you can use the YouTube API to upload those videos to YouTube: https://developers.google.com/youtube/2.0/developers_guide_protocol_uploading_videos