Sadly, it doesn't follow that passing the Senior Candidate exam would have defined Rebecca as a student at the University of Oxford. Apparently the Senior exam was for under-18s, and the Junior exam for under-15s. So these would have been early precursors of what we in the UK now call A levels and GCSE respectively, both part of the General Certificate of Education. (It seems A levels would broadly correspond, in US terms, to a grade 12 high school diploma - although I may be mistaken here, I'm not familiar with the US system.) Those who passed the Senior Exam were given the title "Associate in Arts".
There are fuller narratives here:
Peter Lobbenberg, London