R.R.,
Correction. You wrote "Starting in February of that year (1915) 'Associated Bible Students' was the term used officially." I had looked only at the Feb. 15 issue, but went back to check the Feb. 1 number. This is no doubt what you are inferring to: "Berean Questions In 'Scripture Studies": "The classes of Associated Bible Students throughout the world..." But, this is still referring to the local classes, isn't that correct? For I continue to find references to International Bible Students Association right up to near Russell's death in the Oct. 15, 1916 ZWT. I didn't check after that. On page 306: "I.B.S.A. Berean Bible Studies." On page 307: "What we preach and teach" and specifically "Present Errors and Opposition to Light" where Russell refers to the INTERNATIONAL BIBLE STUDENTS ASSOCIATION.
It seems to me that both names continued to be used throughout up to Rutherford. I suppose the real separation came after Rutherford usurped control.