Problems with re-render component

I have the next situation,

I build a react native app, using design patter: Container-Presentational.

Focus on the problem: When I update props, in component A, I need that the B component change too, when I switch the screen to this B component, I need B component re-render with this new props.

You need to know I am using redux to storage the props, and this component shared navigation.

The main problem is that I cant found one life cycle method where I can re-render component with this new props because the component was rendered, I can´t join in anyone life cycle method.