Yes the LVG seen in the photo flying whilst with the Shuttleworth Collection IS the same machine currently residing in the Beetham Centre at Cosford.
I think I’m right in saying it was one of the WW1 machines that formed the Nash Collection and was loaned to Shuttleworth over 40 years ago. However the Nash Collection (which included the LVG) was transferred/gifted to the RAFMuseum. I think there was negotiation over a delayed transfer enabling it to continue flying.
I have a particular affinity for this aeroplane. As a teenager in the early 1960s I spent holidays camping at Old Warden helping out. The late Bert Etheridge was restoring the LVG back to flying condition and I put a few temporary staples into the lower fuselage ply skinning when it was glued into place :):) happy days.
Roger Smith