Assuming the video is on youtube, ask the IT department to temporarily unblock youtube if the video is on there.
Or try the following:
1) Compose a new PM on the TEF. The recipient should be you.
2) Copy the youtube link into this PM but remove the 's' from the
https part of the link so it becomes
http. For example
https://www.youtube.com/watch?v=cJz7FxCNNho
becomes
http://www.youtube.com/watch?v=cJz7FxCNNho
3) Send the PM. It should then appear in your inbox and will be embedded into the message. Like so:
4) You should be able click on the box to expand it to full screen, the thing the red arrow is pointing to below