It's a brief letter, which is very typical of the Yorks. The letter is signed by Prince Andrew's Assistant Private Secretary, James Upsher. Princesses Beatrice and Eugenie don't have their own household, so all their correspondences are dealt with by Prince Andrew's office. Which is why the stationary features Prince Andrew's Cypher on the letter and envelope.
The reply was written on September 24th, but wasn't mailed till the following week. The reply arrived 65 days (just over 2 months) after I had sent my letter. This is a pretty standard response time.