How did Moshe know of Bilaam's prophecies?

In Bava Batra 16a:

משה כתב ספרו ופרשת בלעם ואיוב

I should note that the statement in the Bavli refers to it as parashat Bilaam, where parsha typically means either some section delineated by petucha and setuma gaps, or else the 1/3rd of a sidra that they leined in Eretz Yisrael. But there are no petuchot or setumot throughout all of parshat Balak, until almost the very end, so it is possible they intended the same thing. The one gap is right before the section on the sin in Shittim and Pinchas' action in perek 25, for which there is no theological difficulty with Moshe having written.

Now, assuming that parshat Bilaam was not a separate sefer, why need to mention it as something Moshe himself wrote? (Indeed, I argue elsewhere that if one just plucks out "parashat Bilaam" there is a nice flow from Chukas to Pinchas.) Of course Moshe wrote it! It is part of "sifro"!

The answer would seem to be that there are large sections of Bilaam's prophecy, and no prophet "steals" another prophet's prophecy.

Ralbag grapples with this:

"And with this the explanation of this parsha is finished.

And before we mention the purposes which come from it, we shall mention one doubt in this matter, which is how the prophecy of Bilaam and the narration of the words of Balak with him is mentioned in the Torah. This doubt is even more increased by virtue of what we find, that Bilaam was already a sorcerer {kosem}.

And we say that this parsha was already mentioned in this place by virtue of the purposes which come from it, for it was already explained from it the force of Divine Providence upon Israel, as we have explained. And for this, the prophet said {Michah 6:5, towards the end of the haftara of Balak}

ה עַמִּי, זְכָר-נָא מַה-יָּעַץ בָּלָק מֶלֶךְ מוֹאָב, וּמֶה-עָנָה אֹתוֹ, בִּלְעָם בֶּן-בְּעוֹר--מִן-הַשִּׁטִּים, עַד-הַגִּלְגָּל, לְמַעַן, דַּעַת צִדְקוֹת ה'.

5 O My people, remember now what Balak king of Moab devised, and what Balaam the son of Beor answered him; from Shittim unto Gilgal, that ye may know the righteous acts of the LORD.

And with this, there is also the purpose of informing what the cause was of the straying of Israel after

illicit relations and after idolatry, and why Israel was commanded to kill the Midianites. And it is fitting that you know that these narratives of Balak and of Bilaam, Moshe pbu"h knew them all from the Mouth of the Almighty, but they were not known to him after they were spread {in natural ways, by word of mouth}. For if not for this, it would not be fitting to write them in the Torah. Behold, just as Moshe related from the Mouth of the Almighty the matter of the narratives of Genesis, so did he relate this narrative which was in this place from the Mouth of the Almighty. And in this manner, the narratives are united with the commandments in the Torah, for all of them are established to bring one to completeness of person drawn to words of the Torah. And to this, za"l {=Chazal} intended by writing that Moshe wrote parashat Bilaam."