Yes, but this is only possible on jitsi.org, not on the university server. A dropbox account is also required.
Alternatively to the procedure described here, recording via OBS Studio would also be possible.
Legal questions regarding recording and publishing cannot be answered here.
1) Click on the three dots at the bottom right and then on "Start Recording".
2) The next step is to connect to a dropbox account where the video will be saved. Then click on "Sart Recording".
3) It may happen that no recording is possible because Jitsi only provides a limited number of recorders at the same time. Unfortunately, the only solution is to wait and see.