"shoulder the task" is correct and usable in written English.
You can use it when you want to express that someone is taking on a responsibility or a job that needs to be done. For example, "John shouldered the task of organizing the event."
Hobsbawm's books, then, will shoulder the task of carrying the name and work forward.
(Colleagues put out the Festschrift in his honor). Hobsbawm's books, then, will shoulder the task of carrying the name and work forward.
The Kurds cannot and will not shoulder the task of liberating areas outside their own, and an alliance with Assad and Iran is actively counterproductive.
Representative Jeffrey J. Teitz told the Legislature in discussing the nominees that its choice would shoulder the task of restoring public confidence in both the Supreme Court and the state's judiciary.
With Bob Carpenter and Peter Zezel, the team's top two checking centers, missing the game (Carpenter has a break in his left foot and Zezel a bruised left foot), Coach Jacques Lemaire chose Denis Pederson to shoulder the task of playing center against Ottawa's top line.
Since the technocratic approach assumes that an intervention aims to produce a certain outcome, then the ascription of responsibility is preordained to taking upon one's shoulder the task to produce (in the sense of bringing into existence) the desired outcome.
Mrs. Vaughan shouldered the task of trying to rescue her daughter from disability.
In the dramatizing of gay rights, somebody needed to include the right of same-sex partners to be as bogged down in moping and pettiness as anyone else, and Sachs has shouldered the task.
The show has been particularly smart in dramatizing Max's effect on everyone around him: the way his condition has at once divided and united his parents, built tricky bridges with his cousins, forced his sister into a good-girl role, and made his mother, Kristina — who shoulders the task of overseeing Max's therapies — anxious and vigilant.
McNamara has not shrunk from shouldering the task.
The Irish Minister for Justice, Equality & Defence, Alan Shatter, told guests at the launch: "The collection records the personal commitment and sacrifice by those men and women who shouldered the task of gaining independence for this country.
