It may be worth contacting these guys: https://www.oldscottish.com/school-leaving-certificates.html
They've started indexing but are still at 1917 so a long way off from the 1940s! This is assuming she sat exams though.
This doesn't look like what you're looking for but is really interesting and is from the school board in the same area:
https://www.mearnshistory.org.uk/index.php/articles/schools/school-leaving-certificate |