Hi, easiest is if you order then again a license from Nexus, and then ecoinvent will check that the university has a license, and share this with us, and then we can give access. The license is technically the same, but for users it does not matter. As you write, every member of the faculty, including the active students, can use ecoinvent then on their personal computers, it is not restricted to university computers.
Hope this helps, best wishes,
Andreas