That would be most remarkable when the King of Prussia (then Wilhelm I, later first German Emperor) would give such an amazing and old treasure directly to Princess Sophie von Württemberg.
This would mean that the King gave his best pearls (I can not imagine that there is a better or more historic pearl collier in the House of Prussia) away. That was not how I understood it, but I stand corrected. Sometimes I feel that Martijn Akkerman is a great expert but makes little mistakes on details, I have heard him so now and then making these mistakes in Tussen Kunst En Kitsch (the Dutch equivalent of the Antiques Roadshow) and I thought: "Hmmm... a bit uncareful with precize details".
But who knows, maybe he has access to all Orange-Nassau jewels and corresponding inventories, invoices, bills and whatever.