The full show was professionally recorded at the 25th Anniversary gala in London last year. Including the celebrations at the end with the original London cast. Then last month (a week before the show stopped) they asked Alistair Brammer (Chris) and Rachelle Ann Go (Gigi) and Tamsin Carroll (Ellen) back in (who already left the show for a year), to shoot some additional footage. I suppose for different camera angles, editing, etc.
At the final performance, a few weeks ago, Cameron Mackintosh said that the footage looks so stunning that there will be a cinema release of it this autumn (2016) and then a dvd.
He also added that a Hollywood film won't be "only in my mind" for long.
The Theatre on Film and Tape Archive (often abbreviated TOFT), a unit of the New York Public Library for the Performing Arts, produces video recordings of New York and regional theater productions, and provides research access at its Lucille Lortel screening room.
You need to have a NYC Library card (but anyone can get it day-of, you don't need to live in NY or pay anything for it). Then you go to the third floor where the have the TOFT screening room (a room with computers where they feed the video source onto your personal screen and you watch with provided headphones).
You will need a reason to need to watch it, but it can usually just be "for a project" or "for character research" and it won't be questioned.