Murray appointed Mauresmo just before his first grass-court event at Queen’s Club, drawing attention for the unusual choice of a female coach. Following his quarterfinal exit at Wimbledon, Mauresmo joined Murray's team in Miami to train for the summer hard-court season.
"We've agreed to work together and I think from both sides we're willing to do what it takes to make it work long term," said Murray to BBC Sport.
"I really enjoy working with her, she's helped me a lot."
"She integrated well with the rest of the team. It's been a good start. Now it's about me producing the results."
The Frenchwoman will be at the U.S. Open with Murray, as will long-time coach and hitting partner Dani Vallverdu.