Accepted answer

To simplify the solution you can do something like this:

<BigText onChange={data => {this.setState({ data })}} />

In the BigText component then you can put some data via this callback like this:

handleInputChange(event) {

    const data = {

    this.setState(data );

And transfer this data to your BigTextMobile component from state:

<BigTextMobile data={} ... />

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