The large diamond necklace on Queen Alexandra's velvet choker is her City of London wedding gift shortened.
In his book on the Queen's diamonds, Hugh Roberts said that HM wore it occasionally on a velvet band as a choker (page 94).
The necklace was inherited by Queen Mary who left it to QEII.
Roberts identified it as the one worn by QEII in Toronto in 2010.
It is one of the few diamond necklaces for which there is information about the carat weight etc.
Queen Mary
The photo of Queen Mary was taken before the coronation in 1911. We know this for certain as some years ago Nellie of RJWMB discovered a copy of the photo published in the
Illustrated London News.
The full photo
Comparison showing both images are from same occasion
After the death of Edward VII Queen Alexandra tried to keep certain jewels but Queen Mary won the battle, except for Queen Victoria's small diamond crown which had been left personally to Queen Alexandra.
Because of the tension I very much doubt if Queen Alexandra would have given Queen Mary one of her necklaces.