Converting stateful React component to stateless functional component: How to implement "componentDidMount" kind of functionality?

Functional stateless components do not have lifecycle methods. You should stick with standard component in this case.

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From React's documentation:

These components must not retain internal state, do not have backing instances, and do not have the component lifecycle methods.

What they said (above), but also consider making a stateful component container and passing props/args to subcomponents which are stateless.