A lovely reply arrived today from the UK. I had written to Princess Beatrice of York for her 29th Birthday earlier this month. The envelope and letter are pretty standard of what we see from the Duke of York's office.
The letter reads:
Dear Miss Daly,
Princess Beatrice of York has asked me to thank you for your kind birthday message. Her Royal Highness is very grateful to you for thinking of her on this occasion.
Princess Beatrice of York sends you her best wishes.
Amanda Thirsk LVOPrivate Secretary to The Duke of York