Difficult to say with certitude, of course, but I think the two brooches are not the same.
First, an aquamarine would look pale on the black and white picture; there would not be a dark spot, like the one visible at the centre of the brooch worn by QEQM (then Duchess of York).
Second, the shapes of the brooches look slightly different: Queen Elizabeth II's brooch is clearly rectangular, while QEQM's brooch looks wider in the middle than on the sides.
Just my opinion, of course.
The brooch worn by QEQM was seen a few times in the early years of the Queen Mother's marriage, i.e. in the 1920s. I think it is the same brooch that she wore pinned on her hat for the christening of her eldest daughter, the current Queen, Elizabeth II, in 1926:
on February 15, 2015, 3:55 pm, in reply to "
