The caa sets and issues the exam papers to the ground examiners.
They then in theory (see above) give the tests to the students mark and then debrief them, then update the application form and sign off they have passed that particular exam.
What actually happens in my experience is there is a filing cabinet with the exams in locked away which the FI's have access to. They then give the exams and debrief etc and then putt he sheets into the training records.
Then at the end of the students course the boss or local examiner comes in a sits down and transfers everything to the form.
It was only after I had left instructing I learned on here that as an FI I wasn't meant to have access to the full set of PPL exams. Or for that matter mark them even if it was using a grid. Then discuss what the student got wrong with them.
Personally I think the authorities should just admit defeat on this one and authorise the FI's to do the whole lot including the form signatures. And the ground examiner act as a oversight and QA checker of the system being used. Unless they move the PPL exams online there is absolutely nothing they can do about the fact that reality doesn't match the standards document