Sarah Janes captioned the snap: "A beautiful reply from the Duchess of York for Beatrice and Edo wedding. Love the photo. Thanks Sarah."
The thank you note penned by Fergie read: "Thank you so much for your amazingly caring and supporting messages for Beatrice and Edo's future happiness.
"It was a glorious day; the sun smiled down on them. We were all delighted to be able to come together and celebrate their love for one another.
"Beatrice looked stunning and Edo handsome - their love shone through.
"We are so happy to welcome Edo into our family and thank him for his love and devotion to Beatrice.
"Thank you for many years of kindness and loyalty."
Beatrice was due to marry Edoardo on May 29, but Covid-19 meant they had to delay the ceremony, instead tying the knot in a secret wedding at Windsor Castle on July 17 in front of just 20 guests.
Her father Prince Andrew walked her down the aisle but did not appear in the wedding photos released by Buckingham Palace.
Her younger sister Eugene is expecting her first child with husband Jack Brooksbank. The couple married in October 2018 and are expecting a baby early next year.
The baby will be Andrew and Fergie's first grandchild, and the ninth great-grandchild for the Queen and Prince Philip.