You have to get the function from the childs prop and call it. As it returns a promise you need to use async/await or return the promise from your test, have a look at docs for more infos. Then test the state of the rendered component.

it("should update item accordingly", async() => {
    const rendered = shallow(React.createElement(Item));
    await rendered.find('someChild).prop('updateItem')('someId')
      item: {blah:'blah'}

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