2018-07-20 21:23:12 UTC
https://www.thegazette.co.uk/notice/3071743 - "In accordance with the direction of HER MAJESTY THE QUEEN Letters Patent have passed the Great Seal of the Realm, dated the 16th July 2018 granting unto Her Majesty’s Grandson, His Royal Highness Prince Henry Charles Albert David of Wales, K.C.V.O., and the heirs male of his body lawfully begotten the dignities of Baron Kilkeel, Earl of Dumbarton, and Duke of Sussex." So does this mean that technically he only became Duke of Sussex on 16th July?
The remainder is to "the heirs male of his body lawfully begotten" - so if the Sussexes have a daughter she will not be in remainder to the dukedom, even if she is the firstborn. Despite the Succession to the Crown Act 2013. And NB that this is of more practical relevance to Sussex than to Cambridge, which will in the normal course of events merge in the Crown, as e.g. the Dukedom of York did in 1910.