"took over the task" is correct and commonly used in written English.
It means to assume control or responsibility for completing a task or assignment. Example: "John was sick, so his colleague Mary had to take over the task of presenting the project to the client."
Casey took over the task of preparing a voluminous report on flood control.
Mr. O'Neal took over the task of merging St . Georgewith Advance Bank.
The New York State Department of Health took over the task of issuing filtration avoidance determinations in 2007.
Residents say that cleanup work by the Parks Department, which took over the task this year, was ineffective.
Instead of helping Steven learn, Jay took over the task and then fumed that he had to do the work himself.
At Los Angeles International Airport, José Platero, a 26-year-old native of El Salvador who is not a United States citizen, was pessimistic about his chances of getting rehired as a screener once the government took over the task.
Paris's current mayor, Bertrand Delanoë, has taken over the task.
The gangs used to provide this service so now the police have sort of taken over the task.
He has made himself, in effect, the museum's chief financial officer, and has taken over the task of dealing with the city, state, and federal bureaucracies.
The Dutch commissarissen and the Italian sindaci, appointed by the shareholders, have taken over the task of supervising the directors and reporting on the wisdom and efficiency of their management to the shareholders.
Since the death of Nin's editor and lifelong champion Gunther Stuhlmann in 2002, Herron has taken over the task of publishing A Cafe in Space, a journal devoted to Nin scholarship.
