Change Date to a string on the local time zone of the device

You could use java.time for this, it is made available to lower Android API levels via Android API Desugaring now.

public static void main(String[] args) {
    // (nearly) your example pattern for output (u is better here)
    final String DATE_FORMAT = "uuuu-MM-dd HH:mm";
    // use it to create an output formatter
    DateTimeFormatter outputDtf = DateTimeFormatter.ofPattern(DATE_FORMAT);
    // your example String
    String exampleDate = "Mon Sep 14 11:30:00 GMT+03:00 2020";
    // parse it with a suitable formatter using a specific pattern and a Locale for names
    DateTimeFormatter parserDtf = DateTimeFormatter.ofPattern("EEE MMM dd HH:mm:ss O uuuu",
                                                                Locale.ENGLISH);
    // then parse the example String
    OffsetDateTime odt = OffsetDateTime.parse(exampleDate, parserDtf);
    // get your local offset (the one of your device)
    ZoneOffset localOffset = OffsetDateTime.now().getOffset();
    // and adjust the offset to your local one
    OffsetDateTime localOdt = odt.withOffsetSameInstant(localOffset);
    // and output it (on android, use log...)
    System.out.println(odt.format(outputDtf));  // example datetime
    System.out.println(localOdt.format(outputDtf)); // same time in local offset
}

This code outputs

2020-09-14 11:30
2020-09-14 10:30

Please note that the output has — of course — taken my current offset, which is UTC+02:00.

Try out the getDefault() method of Locale

public static String dateToString(Date date){
    DateFormat dateFormat = new SimpleDateFormat(General.DATE_FORMAT, Locale.getDefault());
    dateFormat.setTimeZone(TimeZone.getDefault());
    if(date == null)
        return "";
    return dateFormat.format(date);
}

Hope it will work for you. Thank you.

Try set it before

TimeZone.setDefault(TimeZone.getTimeZone("Europe/London"));