Apologies for the late comment Stefan.
I find this a really interesting subject. On the surface it seems likely that Queen Alexandra would have left some jewels to her eldest grandson in the expectation that in due time he would become King. As that grandson was also the then Prince of Wales it would seem plausible that he was left jewels specifically meant to be worn by a Princess of Wales -- for example the gifts from both North and South Wales.
Yet, we know that the emerald earrings (part of the gift of North Wales) were being worn by Queen Elizabeth the Queen Mother (as Duchess of York) from just after the death of Queen Alexandra.
We know from Hugh Roberts' book
The Queen's Diamonds that Queen Alexandra died intestate and that shortly afterwards her jewels were divided among members of the family. Roberts specifically said that the division was based on notations made by Queen Alexandra in her jewel inventory.
So, I suspect that some were designated to go to the Duke of Windsor, and specifically the Welsh jewels such as the badges and the pendant/brooch with the Prince of Wales feathers.
Yet, we know that those jewels are still with the mainline of the British royal family.
The Duke of Windsor has been reported as saying that he did not take any heirlooms from the British royal family, and as no one has yet proved otherwise, I think we have to accept what he said. None of the jewels worn by the Duchess of Windsor have been identified as coming from a British royal collection -- except for the pearl necklace it is said Queen Mary left to the Duke.
From the little verifiable information I have seen on the origin of the Duchess' jewels it is clear that the Duke did supply some of the gemstones. It is quite possible that the Duke was given a number of these on his various tours, especially the one to India. Others, it is known that he purchased.
As far as I know, the Duchess never wore jewels previously worn or owned by Queen Alexandra.