Not sure I quite understand the question but here goes anyway...
(1) If you have a pupil about to start lessons with you who is a complete beginner then you could write your case study as you go along with them - covering their very first 6 -9 months of lessons.
(2) If you have a pupil who was a complete beginner and you have, at this very moment, been teaching them for around 6 months then you have a choice: either write the case study (wholly or partly) retrospectively - looking back at their first 6 months of lessons and then maybe keep the case study going for another few months OR
Summarise their progress and achievements so far and start the case study from now.
It all depends on when you want to take the LRSM really. If all your case studies date from today then obviously it will take you the next 9 months - year to complete them.