The phrase "accepted his assignment" is correct and usable in written English.
You can use it when referring to someone agreeing to take on a specific task or responsibility.
Example: "After reviewing the project details, he accepted his assignment with enthusiasm."
Alternatives: "took on his assignment" or "agreed to his assignment."
Ryan, a Wisconsin congressman, will accept his assignment as Romney's No. 2 at the Republican convention with the biggest speech of his political career - one designed to fire up conservatives while reaching out to independents still uncertain about the Republican team.
CINCINNATI -- Announced INF Brandon Larson accepted his outright assignment to Louisville of the IL.
Though he was not Jordan's first choice, the University of Miami coach signed a five-year, $10 million contract with the Wizards yesterday and accepted his new assignment with relish.
In 1954, Capa reluctantly accepted his final assignment to cover the French conflict in Indochina.
Before his note to me self-destructed, I accepted his final etymological assignment.
He accepted his first acting assignment in April 2005.
Mr. Lowery told parishioners at Central United Methodist Church on Sunday that he "was tempted to get off the plantation," but decided instead to accept his new assignment at Cascade United Methodist Church, also in Atlanta.
After completing his required coursework, Coleman accepted an assignment from his advisor, Professor Colin Hutton, to analyze the mineralogy of the New Idria serpentinite mass within the Franciscan Complex of the California Coast Ranges.
Mr Barofsky accepted the assignment only after his boss made an earthy appeal to his sense of patriotism: "Who else is going to protect the public from what could be a $700 billion clusterfuck of fraud?"Indeed, Mr Barofsky reports that no one in the Treasury Department and almost nobody at the Federal Reserve seemed concerned that some might try to exploit the government's largesse.
