If you wish to record the PIP assessment, you must first get written permission from the Assessment Provider and it will also be up to you to provide the equipment to make 2 identical recordings. 2 old-fashioned cassette recorders would be fine but digital and/or video recordings are not allowed.
It is perfectly legal to carry out recording in secret. However, if you wish to do this you must make very sure that the recording device is not detected. Otherwise you run the risk of the assessment being terminated and the PIP claim with it.
Nothing on this board constitutes legal advice - always consult a professional about specific problems