'the appropriate moment' is correct and can be used in written English. You can use it when you want to describe a moment that is considered fitting for a particular situation. For example: "I waited for the appropriate moment to express my gratitude to my teacher.".
But at the appropriate moment, he was decisive and direct.
"It was the appropriate moment to take a giant step backward".
Then, at the appropriate moment, leave quickly, and timed to arrive at exactly 12 30.
Cocos act like an insurance policy that can be cashed in at the appropriate moment.
"Drop detergent, close lid and relax!" the machine intones at the appropriate moment -- or, for slackers, "Please close the lid".
Spain, the spokesman said, "will at the appropriate moment announce its intentions with respect to state financing for the A350".
At the appropriate moment in the film, indicated by a screen-side light box, you eat or drink its contents.
Ludwig does not simply clarify my doubts with English writing, it enlightens my writing with new possibilities
Simone Ivan Conte
Software Engineer at Adobe, UK