[A brief guide to the Constellations P-Z]
Even though the earliest copy so far discovered was only written shortly after 700 BCE, the text was probably composed sometime between 1200 and 1000 BCE.
The following lists are derived from 'Mul.Apin, An Astronomical Compendium in Cuneiform' by Hermann Hunger and David Pingree, 1989. The locations of the Babylonian stars in terms of the Greek stars are my own attributions.
Mul-Apin divides the stars into northern, equatorial and southern paths:
33 Northern stars on the path of Enlil
The Plough, Enlil, the lead star of the stars of Enlil (Most of Draco)
The Wolf at the seed funnel of the Plough (Head & middle of Draco)
The Old Man, Enmesharra (Perseus)
The Crook, the Crouching god (Auriga)
The Great Twins, Lugalirra and Meslamtaea (Gemini)
The Little Twins, Alammush and Ninezengud (Canis Minor)
The Crab, the seat of Anu (Cancer)
The Lion, Latarak (Leo)
The stars that stands in the breast of the Lion, the King Star (The star Regulus in Leo)
The dusky stars that stand in the tail of the Lion, the Frond of Erua, Zarpanitu (Coma Berenices & the western part of Virgo)
Shupa, Enlil, who decrees the fate of the land (Bootes)
The star before him, the Star of Abundance, the messenger of Ninlil (A star in the western part part of Bootes)
The star behind him, the Star of Dignity, the messenger of Tishpak (A star in the eastern part of Bootes)
The Wagon, Ninlil (The 7 principle stars of Ursa Major)
The star at the shaft of the Wagon, the Fox, Erra, the strong one among the gods (The star Zeta in Ursa Major)
The star at the front of the Wagon, the Ewe, Aya (Probably the star Epsilon in Ursa Major)
The Hitched Yoke, Anu, the great one of the heavens (the star Eta in Ursa Major)
The Wagon of Heaven, Damkianna (Ursa Minor)
The star on its rope, the Heir of the Sublime Temple, the first ranking son of Anu (The star Polaris in Ursa Minor)
The Standing Gods of the E-kur, the Sitting Gods of the E-kur (The western part of Ophiuchus; Corona Borealis)
The She-Goat, Gula (Lyra)
The star before the She-Goat, the Sitting Dog (Most of Hercules)
The bright star of the She-Goat, Lamma, the messenger of Baba (The star Vega in Lyra)
Two stars behind her, Ninsar and Erragal (The stars Beta & Gamma in Lyra)
The Panther, Nergal (Most of Cygnus & probably part of Cepheus)
The star to his right, the Swine, Damu (Probably Delphinus)
The star to his left, the Horse (front legs of Pegasus & Lacerta)
The star behind him, the Stag, messenger of the Star Cluster (Cassiopeia & part of Andromeda)
The dusky stars at the breast of the Stag, Harriru, god of the Rainbow (The spiral galaxy M31 in Andromeda)
The bright red star at the kidney of the Stag, the Destroyer (The star Gamma in Cassiopeia)
23 Equatorial stars on the Path of Anu
The Field, the seat of Ea, which leads the stars of Anu (The 4 stars of the Square of Pegasus)
The star at the Field, the Swallow (The head & neck of Pegasus, & the western fish of Pisces)
The star behind the Field, Anunitum (The northern fish of Pisces)
The star behind it, the Hired Man, Dumuzi (Aries)
The Star Cluster, the Seven Gods, the great gods (The Pleiades)
The Bull of Heaven, the Bull's Jaw, the Crown of Anu (Taurus, or at least its head)
The True Shepherd of Anu, Papsukal, the messenger of Anu and Ishtar (Orion)
The Twins who are opposite the True Shepherd of Anu, Lulal and Latarak (Cetus & part of Eridanus)
The star behind him, the Rooster (Lepus)
The Arrow, the arrow of the great god Ninurta (The star Sirius & probably other stars in Canis Major)
The Bow, the Elamite Ishtar, the daughter of Anu (Puppis)
The Serpent, Ningishzida, lord of the Underworld (Hydra)
The Raven, the star of Adad (Corvus)
The Furrow, Shala with her ear of barley (The eastern part of Virgo)
The Scales, the Horn of the Scorpion (Libra)
Zababa, the Eagle and the Dead Man (The eastern part of Ophiuchus; Aquilla; Sagitta)
15 Southern stars on the Path of Ea
The Fish, Ea, the lead star of the stars of Ea (Pisces Austrinus)
The Great One, Ea. The Star of Eridu, Ea (Aquarius; Vela)
The star to his right, Ninmah (Vela)
The Wild Boar, Ningirsu (Most of Centaurus)
The star to its side, the Harrow, the weapon of Mar-biti, within which one sees the Abyss (The western part of Centaurus)
The two stars that are behind him, Shullat and Hanish, Shamas and Adad (Two stars in Centaurus)
The star behind them, rises like Ea and sets like Ea, Numushda, Adad (Unknown, possibly part of the Milky Way)
The star to the left of the Scorpion, the Mad Dog, Kusu (Lupus)
The Scorpion, Ishhara, the governess of the lands (Scorpio)
The Breast of the Scorpion, Lisi and Nabu (The star Antares in Scorpio)
The two stars on the Stinger of the Scorpion, Sharur and Shargaz (The stars Lambda and Nu in Scorpio)
The star behind them, Pabilsag (Sagittarius)
The Cargo-Boat and the Goatfish (Corona Australis; Capricorn)