The Starter Checklist, which replaces the old P46, is only about telling HMRC (through the employer's wages department) what taxable income has been received since the start of the current tax year. i.e. it only looks backwards in time, not forwards. So, as far as the form is concerned, the fact that your FIL will start to receive two pensions in the near future is irrelevant.
So the correct answer to Q.9 is 'No'.
As your FIL has been receiving ESA, the answer to Q.10 is 'Yes', meaning that he then needs to put a cross under 'Statement B'. (It's the 'and/or' bit there which applies to him).
That will satisfactorily comply with the requirements of the form but, when submitting it, it might be best to enclose a covering letter to advise the employer that there will be a further change in your FIL's tax status in the very near future (due to the commencement of both pensions).