I received this reply a year and a half ago. I had written to Princess Sofia of Sweden for her birthday. I rarely write to the Swedish Royals, as they don't often reply. But Prince Carl Philip & Princess Sofia's office does regularly send out birthday replies.
The envelope is the usual from the Swedish Royals. With the Royal Coat of Arms in the upper left corner, with "Royal Court" and the partial address underneath. The back of the envelope is blank.
The letter is pretty identical to Princess Sofia's birthday replies from past years.
The letter says:
Royal Palace, Stockholm
25 February 2021
Gertrude A. Daly
[My address]
Dear Miss Daly,
Her Royal Highness Princess Sofia has asked me to thank you for the kind greeting on the occasion of Her birthday together with the well wishes.
Yours sincerely,
Anita SöderlindSecretary to HRH Princess Sofia