The singer, who signed to Moss' agency last year (18), posed for the snap next to a sleeping Kate.
She added the caption: "There's only one KM. Happy birthday!! You do so much for so many here's to your day! you deserve the world!"
"I love you always and forever and I'm so happy to call you my friend. Here's to many more memories and laughs!"
Moss marked her 45th birthday on Wednesday following a night out at The Dorchester hotel in London, where Ora and Kate were joined by the model's boyfriend Count Nikolai Von Bismarck and best pal Stella McCartney.