The Assessment Providers for PIP do not offer any recording facilities for PIP it is down to the claimant to provide the equipment and to seek permission.
You can legally record a telephone conversation without having to inform the other party provided that it is being made for personal use only, in fact, if you tell the assessor they will almost certainly refuse permission and may terminate the telephone interview if they believe that you are doing so.
Gordon
Nothing on this board constitutes legal advice - always consult a professional about specific problems