I do not know the origin of this set. Probably beautiful stones, but the whole design looks a bit bling-bling to my taste...
I have another picture from this necklace. The picture posted by Poliester is the only occasion for which I saw the Princess of Naples with this necklace, which would make me favour the hypothesis of a loan - but it is just a guess.
(I have had this picture in my files for a very long time, and I did not noted from where I got it - it somehow looks like a picture from an auction website)