Youtube – Sharing someone else’s YouTube video to someone else’s public playlist if I have the link

First, your teacher should add you as collaborator of the playlist. Then (from Collaborate on playlists - Youtube Help):

Contribute videos to a playlist

Once you’ve been invited to contribute to a playlist, you can add videos or remove videos that you added in the past.

Add videos

1. Use the link you got from the playlist owner to go the playlist page.
2. Follow the on-screen instructions to confirm that you want to be a contributor. The playlist will be automatically saved.

3. To add videos from your computer or a mobile device, use one of these options:

   • On the playlist page, select Add Video and paste in a video URL, choose a video from your uploads, or search for a video on YouTube.
   • Go to a video you want to add and select the Add to menu from that video.

After you add a video, your name will appear next to the video in the playlist. All collaborators will get a notification when new videos are added to the playlist.