Yesterday, I received a letter from Denmark. Inside was a note from one of Crown Princess Mary's Lady-in-Waiting thanking me for writing to Crown Princess Mary on the occasion of her 43rd Birthday. It is a generic thank you they send to everyone who wrote for that occasion.
I sent the letter on Feb 4th, they sent their reply on Feb 10th, and 42 days latter I received it in the mail. The Denmark Royals are the only Royals I have encountered, so far, who send their letters Economy. Other Royals send their letters Priority or First Class. Those usually arrive in the US a week after their reply is sent.
I was however surprised by how quickly they responded to my letter, that was the quickest response yet by any Royal. Usually it can take 14 to 67 days, from when I sent the letter for them to send a reply (Based off of the Postmark).
This note was very similar to the one I received for writing to the Crown Prince Couple (Prince Frederik and Princess Mary) for Christmas.