Additionally, it's important to draw a distinction between works attributed to Enheduanna and the works that were actually composed by Enheduanna. Most of the works attributed to Enheduanna were in fact created in the Old Babylonian period, several hundred years after the collapse of the Akkadian empire.

>For the Sumerian corpus, the tradition gives us the names of two alleged authors: Enheduanna and Lu-Inanna (Michałowski 1996: 183–86). Enheduanna was the daughter of Sargon, the king of Akkad, as well as a priestess of the Moon-god Nanna at Ur. Up to six compositions are attributed to her: a long hymn to Inanna known as The Exaltation of Inanna or Ninmešarra (nin me šar2-ra “lady of all the me’s/divine powers”; Zgoll 1997); Inanna hymn C or Inninšagurra (in-nin ša3-gur4-ra “lady with a great heart”; Sjöberg 1975a); the narrative known as Inanna and Ebih (Attinger 1998); the collection of Temple Hymns (Sjöberg and Bergmann 1969); a balbale song of Nanna; and an Ur III tablet mentioning Nanna-Suen and Enheduanna (Goodnick Westenholz 1989).

>However, the main composition attributed to her that includes some possibly autobiographical data (Ninmešarra) was most likely composed several centuries after Enheduanna’s death, in the Old Babylonian period (Civil 1980: 229). Aside from the aforementioned Ur III text, no composition traditionally attributed to her appears in a single tablet that could be dated prior to 1800 (Veldhuis 2003: 31 n. 2). In fact, there can be little doubt that Enheduanna started to be regarded as an author only in a tradition that begins centuries after her death: This is a case of traditional authorship, not historical. The other supposed author is Lu-Inanna, “chief leatherworker (ašgab gal) of Enlil,” who according to the composition itself would have dictated the Tummal Chronicle to a scribe (Sollberger 1962; Oelsner 2003). However, this composition is not the historical document that it purports to be but rather a scribal artifact. Thus, the attribution of its authorship to a leatherworker is an ironic device within an erudite exercise in fake royal legitimation...

"Sumerian Literature" by Gonzalo Rubio in From an Antique Land: An Introduction to Ancient Near Eastern Literature edited by Carl Ehrlich