Edit in JSFiddle

class TodoApp extends React.Component {
  constructor(props) {
    super(props)
    this.state = {
      listA: [0,1,2,3,4],
      listB: [5,6,7,8,9],
    }
    this.moveAtoB = this.moveAtoB.bind(this);
  }
  
  moveAtoB(movedItem) {
  	//remove from A
    this.setState((previousState, previousProps) => ({
    	listA: previousState.listA.filter(item => item !== movedItem),
    }), () => console.log(this.state.listA));
    //add to B not working
    this.setState((previousState, previousProps) => ({
    	listB: previousState.listB.push(movedItem),
    }), () => console.log(this.state.listB));
  }
  
  render() {
    return (
      <div>
        <div className="list">
          <h2>List A:</h2>
          <ol>
          {this.state.listA.map(item => (
            <li key={item}>
              {item} 
              <button onClick={() => this.moveAtoB(item)}>-></button>
            </li>
          ))}
          </ol>
        </div>
        <div className="list">
          <h2>List B:</h2>
          <ol>
          {this.state.listB.map(item => (
            <li key={item}>
              {item} 
            </li>
          ))}
          </ol>
        </div>
      </div>
    )
  }
}

ReactDOM.render(<TodoApp />, document.querySelector("#app"))