They should be the one to set up their RTI submission to their own gateway. Then, the accountant can submit the RTI once payroll is done. The Authorization for HMRC Gateway ID is only applicable for submitting VAT return MTD.
You’ll need an HMRC credentials and HMRC reference to make sure that your payroll tax information is submitted to HMRC. The RTI status will now show as Complete on the Payroll home page.