He is planning to "work" for two employers simultaneously; He is approved for serial employment which implies he would leave one before beginning at the second.
Many employers expect the employee to work after a vacation in order to receive pay for that vacation pay. Some employers also include vacation pay in the last check upon employee termination. OP needs to check company policies; it is that simple. I find his proposal to not disclose to his first employer that he has begun working elsewhere dishonest. An employer would be justify terminating him "for cause".