public class TaskA implements Runnable {
    @Resource
    private TaskService taskService;

    @Override
    public void run() {
        // Run task A
        // ...

        // Set run ID for task B to retrieve
        taskService.setRunId("A", UUID.randomUUID().toString());
    }
}

public class TaskB implements Runnable {
    private static final Logger log = LoggerFactory.getLogger(TaskB.class);

    @Resource
    private TaskService taskService;

    private String lastId;

    @Override
    public void run() {
        String nextId = taskService.getRunId("A");
        if (this.lastId == null) {
            log.info("First run. Not executing");
        } else if (lastId.equals(nextId)) {
            log.warn("Task A has not run. Refusing to execute");
        } else {
            log.info("Executing");
            // Run task B
            // ...
        }
        this.lastId = nextId;
    }
}