def chat_migration(update, context):
    m = update.message
    dp = context.dispatcher

    # Get old and new chat ids
    old_id = m.chat_id or m.migrate_from_chat_id
    new_id = m.migrate_to_chat_id or m.chat_id

    # transfer data, if old data is still present
    if old_id in dp.chat_data:
        dp.chat_data[new_id].update(dp.chat_data.get(old_id))
        del dp.chat_data[old_id]

...

def main():
    updater = Updater("TOKEN", use_context=True)
    dp = updater.dispatcher

    dp.add_handler(MessageHandler(Filters.status_update.migrate, chat_migration))

...

def error(update, context):
    """Log Errors caused by Updates."""
    logger.warning('Update "%s" caused error "%s"', update, context.error)

    if isinstance(context.error, ChatMigrated):
        new_chat_id = context.error.new_chat_id

def my_callback(update, context):
    dp = context.dispatcher

    ...

    try:
        context.bot.send_message(chat_id, text)
    except ChatMigrated as e:
        new_id = e.new_chat_id

        # Resend to new chat id
        context.bot.send_message(new_id, text)

        # Transfer data
        if chat_id in dp.chat_data:
            dp.chat_data[new_id].update(dp.chat_data.get(chat_id))
            del dp.chat_data[chat_id]

    ...