def METHOD_NAME(target_sat, clean_root_mailbox, long_running_task):
    """Wait until the long-running task ID is found in the Satellite's mbox file."""
    timeout = 300
    try:
        wait_for(
            func=target_sat.execute,
            func_args=[f'grep --quiet {long_running_task["task"]["id"]} {clean_root_mailbox}'],
            fail_condition=lambda res: res.status == 0,
            timeout=timeout,
            delay=5,
        )
    except TimedOutError:
        raise AssertionError(
            f'No notification e-mail with long-running task ID {long_running_task["task"]["id"]} '
            f'has arrived to {clean_root_mailbox} after {timeout} seconds.'
        )
    return True