Hi Fiona,
It's great that you got the book and are enjoying it!
FrGrH is fairly common shorthand for "Die Fragmente der griechischen Historiker" (The Fragments of the Greek Historians) compiled by F. Jacoby. The fragments of the ancient Greek historians of Alexander are in Part II B, pp. 618-828 (Berlin, 1929). Actually, the original collection of the fragments of the Alexander historians was compiled by Karl Muller and published as an addendum to the Didot edition of Arrian in Paris in 1846. Jacoby simply completed and sometimes modified Muller. In fact, the history of Alexander histories is almost as complicated as the history of Alexander himself

The fragments fall into several classes. Firstly there are the Testimonies, which provide information about Cleitarchus himself. Secondly, there are the Fragments proper, and these are divided into fragments with a book number, other relatively reliable fragments and finally doubtful fragments. Fragments are essentially defined as ancient Greek or Latin texts where the immediate author states that Cleitarchus wrote the material in the fragment. In most cases it is very clear that it is the famous author of the History of Alexander that they are referring to.
It would be fair to say that my long essay on the basis for the reconstruction in Chapter 2 sometimes gets a bit abstruse, because it has to deal with some very complicated issues. Some people may find it more interesting to read the reconstruction itself in Chapters 3 to 5 first, then come back to Chapter 2 to find out as much as they want about how it was formulated.
Best wishes,
Andrew