HRH is for a Princess... King's Lynn twitter made the embarrassing mistake. Her Majesty for The Queen.
A Monarch's children in the male line are automatically an HRH. That means The Queen's sons could all claim that distinction for their children but Elizabeth II's only daughter, Princess Anne (The Princess Royal), couldn't. So William, Harry, Beatrice and Eugenie are all HRHs because they are the children of sons of the Monarch.
Monarchs and their consorts are usually called Majesty.