Bill
I assume that he is receiving Income Related ESA?
The issue will be how the DWP handle his current claim for ESA, if they simply suspend payment then it should be no problem backdating payments if he is successful in applying for PIP, however, if the claim is closed then a new claim can only be back dated by three months, if this covers the PIP Decision then there would be no problem, but if does not and the money is significant enough to be wanted, then the only way forward would likely be to challenge the Decision that closed the claim, how this would be handled, given that the facts on which the Decision was made will have changed, I do not know.
Gordon
Nothing on this board constitutes legal advice - always consult a professional about specific problems