DadsTools, so are you saying you thought Wayne or SK started the BF? Or the Japanese BF vendor just copied the original trufit tools and then continued making their own other tools in addition? I'm going to continue posting the older BF tools I have or come across, also.
The latter. When Wayne discontinued the LC TruFit model wrenches shortly after its purchase of LC in 1962, Sears was forced to find another supplier for its SEARS branded budget end wrench line. Sears turned to a Japanese mfr for this, which made for Sears EXACT copies of the discontinued TruFit-style wrenches. To the best of my research, these are the first Sears tools to bear the BF JAPAN markings, and were first offered for sale around 1963-64. Sears was apparently happy with the results, because it started having BF make a number of other tools (including vises). Some of these were exact copies of what Sears had been sourcing from other mfrs, as davethorik pointed out with his Columbian vise clone by BF. Most folks recall that the Sears BF tools were fairly good quality, so Sears' decision to expand its use of the BF JAPAN mfr was apparently a good one.
GJ Member lauver's incredible list of Craftsman mfr codes and dates, which many of us use as a guide, lists the BF mark as 1969-87. While this date might refer only to CRAFTSMAN marked tools, Sears' use of the BF mfr dates earlier back to 1963-64 with the TruFit wrench clones. Again, based on my research, these are the first Sears BF tools.
While lauver has offered a few possible Japanese tool mfrs as the source for the BF tools, to my understanding no one has been able to definitively identify that mfr. The reason for this may be that BF produced for Sears only unique designs or exact copies of other mfr's tools, so we may not have a Japanese branded tool that we can compare to a Sears-branded tool and say "There's a match."