In Plato's Phaedo (98b), Socrates says he read books (plural in the Greek) by Anaxagoras, and at Apology (26d) he says these books can "sometimes be bought in the orchestra for many drachmas." (The orchestra was the area for the chorus in a theater, "Sometimes" renders the Greek word "eniote.") There is no reason that books Socrates read could not have survived to Plato's time, but so far as I know there is no evidence books by Anaxagoras did survive either. Aristotle gives fragments of Anaxagoras.
Is there evidence that whole books of Anaxagoras were still circulating in 4th century Athens? Is there evidence that Plato would have seen them? What are good sources on these questions?
Of course the plural on "books" here is compatible with the ancient authors who (according to Stanford Encyclopedia) say Anaxagoras only wrote one book, since "book" here could mean what were later called chapters of one book.
The question naturally expanded in the comments to whether Simplicius (ca. 480–560 CE) saw Anaxagoras' book.
I accepted an answer because I think it (together with Conifold's comment) does reflect the state of the evidence, though I think that answer draws far too strong a conclusion from the evidence.
It is normal in philosophy, and also in classics, to give and discuss evidence.
So, for example, a comment by b_a notes that the standard reference Diels-Kranz cites specific passages of works as sources for each fragment of Anaxagoras. Those sources are Plato, Aristotle, Theophrastus, Simplicius and others. Neither those ancient authors, nor Diels-Kranz have citations to Anaxagoras directly. So Simplicius will write of "The last book of Aristotle's Physics, which is the eight by number of the entire treatise." He cites the tenth book of Plato's Laws as "The tenth of the Laws." I call those citing Aristotle and Plato's works directly. But so far as I see his references to Anaxagoras are never like that but all of the form "Anaxagoras says." Now that does not prove he was not looking at the entirety of a book by Anaxagoras. But neither does it prove he was.
Diels and Kranz cite this evidence perhaps partly to overcome reasonable (or unreasonable) doubts, but more because it is interesting, and because it lets people look further into the questions. That evidence fully justifies McKirahan saying Simplicus 600 years after Plato "had the text (or at least some of the text) of Anaxagoras before him" (cited in a comment by b_a). McKirahan's parenthetic disclaimer explicitly leaves open the question of whether Simplicius had the full book of Anaxagoras or fragments of it.
The comment by Conifold gives very intriguing textual evidence with a link. At that link you see they are not sure of the translation saying Epicurus "ordered" the best works of Anaxagoras--but it is likely the word was some form of "lambano" and would mean some kind of holding or having so this does not make much difference for my question.
The frustrating point of this text for me is that the phrase "the best works" is represented on the papyrus by just "beltis" which is part of the Greek word for "best." Both the article and the word ending are missing so that I do not see how you can even tell "best" here is a plural, let alone tell whether it means the best books, or best chapters, or best collected quotes of Anaxagoras. If anyone does see how the Greek in this fragment settles that question I will be grateful.
In sum the evidence suggests Plato did see Anaxagoras's book and Simplicius may have. But the strongest textual evidence is in Plato, where it is not very explicit. The rest of the textual evidence is quite thin and requires heavy interpretation.
As to expert opinion, Barnes writing in the 1970s roundly excoriates anyone who would claim "The so-called fragments are assuredly far from direct quotes from Anaxagoras’ book." I have never seen anyone claim that though. I have never seen anyone even hint that Simplicius' fragments are not actual quotes. The question is whether Simplicius had Anaxagoras's book in front of him. And the only people I see assured of what happen are those who think Simplicius assuredly did have it.
That notably includes Burnet writing in 1924 as quoted by sand1 in a comment saying "Simplicius had access to a copy, doubtless in the library of the Academy". Scholars today succeed at doubting all such specific claims about what was ever in the academy.
Burnet had a lot of views on this topic that few people today share, most relevantly here: "Burnet was known for defending novel interpretations of Plato and Socrates, particularly the view that the depiction of Socrates in all of Plato's dialogues is historically accurate... Burnet believed that Socrates had been in his youth the disciple of Archelaus, a member of the Anaxagorean tradition."
I remain persuaded that McKirahan published his parenthetical disclaimer that Simplicus saw "the text (or at least some of the text) of Anaxagoras" because he believed the state of the evidence demanded it. And I believe the evidence does demand it.