The phrase "repeat after him" is correct and can be used in written English.
It is typically used in instructional or educational situations, when someone is teaching or demonstrating something and wants the listener to repeat it back to them for practice or clarification. Example: "The teacher said, 'repeat after me', and the students repeated the sentence to practice their pronunciation."
I repeat after him the prayer for the dead.
He asked her to repeat after him the first lesson, titled "A Private Conversation".
He paused so that his students could repeat after him, as if they were reciting some madcap catechism.
He asked her to repeat after him the first lesson, titled "A Private Conversation". Her body tensed at the closeness of their shoulders and thighs as they bent over the book.
Then he waved it over his head like a lasso, gesturing me to repeat after him in a prayer that meant, roughly: "This is my exchange, this is my substitute, this is my atonement.
He then told the crowd to repeat after him: "I do solemnly swear that I — no matter how I feel, no matter what the conditions, if there's hurricanes or whatever — will vote, on or before the 12th for Donald J. Trump for president". Jewish groups complained at the time about the disconcerting imagery of people raising their right arms in what looked like a Nazi salute.
"No tea," I repeated after him.
Olcott led the students through the Veterinarian's Oath, which the third-years repeated after him, right hands raised.
"Ku-kul-kan," he said, pronouncing each syllable separately and banging slowly on a drum as his listeners repeated after him.
We repeated after him, and, after placing our sandals in shoe racks, entered through the Gate of Peace into the Grand Mosque, a white-and-gray marble complex with an octagonal courtyard and multilevel prayer spaces, crowned by minarets.
As the first ball is offered, the priest says (and the son repeats after him), "May this create a head"; with the second ball, "May this create neck and shoulders"; with the third, "May this create heart and chest"; and so on.
