Charles said:
HM and HRM are equivalents.
That's why kings who are also emperors are sometimes called "Imperial & Royal Majesty".
Sometimes, but in those cases it was done to highlight the fact that the individual in question was both an Emperor and a King. No such distinction applies to HM QE II or any of the other European monarch, since as you know, there are no dual Emperor-Kings.
Second even when there were, they were not really addressed as such (with the exception of the German Emperor, but not even always then). The Emperor of Austria was simply HIM Majesty und Apostolic Majesty (for Hungary, after St. Stephen). Or, more properly, after 1868 he was
Kaiser von Österreich, König von Böhmen u. s. w. und Apostolischer König von Ungarn or in abbreviated form
Kaiser von Österreich und Apostolischer König von Ungarn with the style of
Seine Majestät der Kaiser und König or
Seine k. u. k. (kaiserliche und königliche) Apostolische Majestät. (
http://www.heraldica.org/topics/royalty/royalstyle.htm#austria)
(Although, the Archdukes and Archduchesses were Imperial and Royal Highnesses after the introduction of the dual monarchy.)
In Russia the Czar was simply his HIM, and in Germany the Kaiser was also addressed as HIM, although he was properly Kaiserliche und Königliche Majestät -- or His Imperial and Royal Majesty,for the reason stated above. In Britian, the monarch remained HM, despite being Empress/Emperor of India from the 1870s to the 1940s. They weren't allowed the style of HIM, although I believe it was debated in Parliament ( I will have to check my sources for exact dates)
For QE II, a style of Royal Majesty is be redundant, as the Majesty already implies that she is royal. It would be like referring to her as " Your Royal Royal Majesty". If that makes any sense.

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