No, the employment letter was a requirement. Just submitting the payslips wasn't sufficient and he had to prove that he is working which can only be proven with a job letter.The payslips help, however the job letter says what you’re position is, and how much you make. This is important to know, but hey pay slips are also good. Wait for the AOR, without it there is no point in getting stressed.
That said, the only solution is to wait for an AOR (if you get it) and submit the letter via the web form.