Sotheby's have the answer for you, Tilia C.
"The Princess’s three sons, Prince Emanuele Filiberto, future Duke of Aosta (1869-1931), Prince Vittorio Emanuele (1870-1946), Count of Turin, and Prince Luigi Amedeo (1873-1933), Duke of the Abruzzi, would have inherited their mothers jewel collection. Princess Hélène of France, the wife of her eldest son, Emanuele Filiberto, is believed to have never worn the tiara. Therefore, historians assume that it must have gone to one of her other sons, either the Count of Turin or the Duke of the Abruzzi, both of whom died without descendants. It is known that King Umberto II of Italy bought the jewel from one of his cousins to prevent this historic piece from leaving the family collection."
It must've been given/left to Princess Maria Gabriella by her father, who, ironically, bought it so it could stay in the family.