The bracket is Abus specific and must match a plastic counterpart piece that appears on all Abus U-locks and at least some of their non U-Locks. (Presumably you can go to the Abus site and magnify photos to see details.) However, I have seen such pieces on some generic U-locks, where a company seemingly decided to follow the Abus suit rather than invent the wheel on their own. In my memory, I had no problem mounting such a non-Abus lock on an Abus bracket. The piece from the U-lock side allows to slide the lock onto the bracket attached to the frame. I do not know whether you can buy such a piece for the U-lock side separately.

P.S. Just in case I misunderstood your question, I bought the TexKF bracket (on the frame side) separately from the lock.