The director of the Museum of the Bible/Green Collection, David Trobisch, has kindly informed me via email that the collection is going towards full digitisation and open access. As it happens in many other collections, “in some cases items are put on reserve and not accessible until the research has been done.” He writes that information on the acquisition circumstances of the Green Sappho fragments and their relation with the London Sappho will be provided in a forthcoming publication by Dirk Obbink.
As for the acquisition circumstances of Galatians 2 (GC 462), the Green collection has purchased it “through a trusted dealer that we have done business with over many years”.
I thank David Trobisch for the answers he is constantly providing; it is clear that his arrival is a dramatic step forward for the Green Collection. My only comment is that this dealer must not be so trustworthy since the papyrus was on sale from e-Bay Turkish seller MixAntik in 2012.