"The Queen and the Duke of Edinburgh would like to be remembered to you." - what does that mean?
Solution 1:
The Oxford Dictionary gives one meaning of remember as
1.3 (remember someone to) Convey greetings from one person to (another).
So the sentence
The Queen and the Duke of Edinburgh would like to be remembered to you.
means
The Queen and the Duke of Edinburgh would like convey their greetings.
This seems quite a stilted and formal statement, but this is royal protocol.
Solution 2:
It is so unfortunate that “remember me to ___” is going out of fashion. It is such a good way of saying
Let ——- know that I say hello.
In fact, it means more than just "hello", it’s fonder with a hint of respect. It sounds very formal but many times I’ve heard this colloquially used in Nottinghamshire growing up. Very pleasant to the ear.