React Native: Propagate Pan Responder event from view to inner scroll view

/**
 * Sample React Native App
 * https://github.com/facebook/react-native
 *
 * @format
 * @flow
 */

import React, { Component } from 'react';
import { Platform, StyleSheet, Text, View, Dimensions, PanResponder, Animated, ScrollView } from 'react-native';

const instructions = Platform.select({
  ios: 'Press Cmd+R to reload,\n' + 'Cmd+D or shake for dev menu',
  android:
    'Double tap R on your keyboard to reload,\n' +
    'Shake or press menu button for dev menu',
});

export default class App extends Component {

  constructor(props) {
    super(props);
    
    const {height, width} = Dimensions.get('window');

    const initialPosition = {x: 0, y: height - 70}
    const position = new Animated.ValueXY(initialPosition);

    const parentResponder = PanResponder.create({
      onMoveShouldSetPanResponderCapture: (e, gestureState) => {
        return false
      },
      onStartShouldSetPanResponder: () => false,
      onMoveShouldSetPanResponder: (e, gestureState) =>  {
        if (this.state.toTop) {
          return gestureState.dy > 6
        } else {
          return gestureState.dy < -6
        }
      },
      onPanResponderTerminationRequest: () => false,
      onPanResponderMove: (evt, gestureState) => {
        let newy = gestureState.dy
        if (this.state.toTop && newy < 0 ) return
        if (this.state.toTop) {
          position.setValue({x: 0, y: newy});
        } else {
          position.setValue({x: 0, y: initialPosition.y + newy});
        }
      },
      onPanResponderRelease: (evt, gestureState) => {
        if (this.state.toTop) {
          if (gestureState.dy > 50) {
            this.snapToBottom(initialPosition)
          } else {
            this.snapToTop()
          }
        } else {
          if (gestureState.dy < -90) {
            this.snapToTop()
          } else {
            this.snapToBottom(initialPosition)
          }
        }
      },
    });

    this.offset = 0;
    this.parentResponder = parentResponder;
    this.state = { position, toTop: false };
  }

  snapToTop = () => {
    Animated.timing(this.state.position, {
      toValue: {x: 0, y: 0},
      duration: 300,
    }).start(() => {});
    this.setState({ toTop: true })
  }

  snapToBottom = (initialPosition) => {
    Animated.timing(this.state.position, {
      toValue: initialPosition,
      duration: 150,
    }).start(() => {});
    this.setState({ toTop: false })
  }

  hasReachedTop({layoutMeasurement, contentOffset, contentSize}){
    return contentOffset.y == 0;
  }

  render() {
    const {height} = Dimensions.get('window');

    return (
      <View style={styles.container}>
        <Text style={styles.welcome}>Welcome to React Native!</Text>
        <Text style={styles.instructions}>To get started, edit App.js</Text>
        <Text style={styles.instructions}>{instructions}</Text>
        <Animated.View style={[styles.draggable, { height }, this.state.position.getLayout()]} {...this.parentResponder.panHandlers}>
          <Text style={styles.dragHandle}>=</Text>
          <ScrollView style={styles.scroll}>
            <Text style={{fontSize:44}}>Lorem Ipsum</Text>
            <Text style={{fontSize:44}}>dolor sit amet</Text>
            <Text style={{fontSize:44}}>consectetur adipiscing elit.</Text>
            <Text style={{fontSize:44}}>In ut ullamcorper leo.</Text>
            <Text style={{fontSize:44}}>Sed sed hendrerit nulla,</Text>
            <Text style={{fontSize:44}}>sed ullamcorper nisi.</Text>
            <Text style={{fontSize:44}}>Mauris nec eros luctus</Text>
            <Text style={{fontSize:44}}>leo vulputate ullamcorper</Text>
            <Text style={{fontSize:44}}>et commodo nulla.</Text>
            <Text style={{fontSize:44}}>Nullam id turpis vitae</Text>
            <Text style={{fontSize:44}}>risus aliquet dignissim</Text>
            <Text style={{fontSize:44}}>at eget quam.</Text>
            <Text style={{fontSize:44}}>Nulla facilisi.</Text>
            <Text style={{fontSize:44}}>Vivamus luctus lacus</Text>
            <Text style={{fontSize:44}}>eu efficitur mattis</Text>
          </ScrollView>
        </Animated.View>
      </View>
    );
  }
}

const styles = StyleSheet.create({
  container: {
    flex: 1,
    justifyContent: 'center',
    alignItems: 'center',
    backgroundColor: '#F5FCFF',
  },
  welcome: {
    fontSize: 20,
    textAlign: 'center',
    margin: 10,
  },
  instructions: {
    textAlign: 'center',
    color: '#333333',
    marginBottom: 5,
  },
  draggable: {
      position: 'absolute',
      right: 0,
      backgroundColor: 'skyblue',
      alignItems: 'center'
  },
  dragHandle: {
    fontSize: 22,
    color: '#707070',
    height: 60
  },
  scroll: {
    paddingLeft: 10,
    paddingRight: 10
  }
});