Dear Shri TBT, I have also no case that Vaalmeeki copied anything from any Greek books. Simply put, this first hindu epic was inspired by the epic poetry genre of the Greeks, imho.
Oops! you are wrong about history and civilizations too !
Beginning of Ancient Greece was about 500 BC, which was earlier a cenfedaration of Indo-european (sanskrit/Slavic speaking ) tribes who have migrated from northern asia to europe to norway and down south to Greece/Italy. The Attic/Atheneas/Ionians led the greece to wage a war against all these tribes who also allied some tribes (phyrgians/Bhrges(Bhrigu clan), the Trojans (the hittites) on the western Anatolia/Turkey. The latter were also supported by the 2000 year old goddess, Mahishasura like worshipping , early writers (linear B) of the Crete Islands in the south of Greece. The story of Helen may be a fabrication on the characters with the real war happening, as the Early Greeks were taking over the area.
Homer's was a great inspiration for Greek Writing , Art, and literature, only becos the myths were already a mix of all past tribes. Whereas, the hittites/hurrians (with both sanskrit, persian, sumerian mixed language - Turvisa,wilusia, larshiya, purushuttam,parana etc.) had a early writing and Cretians had linear A writing (with phonetics), Newly forming Turkish (leaving out sanskrit 'sh' - truva, wiluva, lariya, ahuwa etc.) Greek only made it (troy, illiad, lycia).
Sumerians, in the south of Turkey/mesopotomia/Persian gulf were the earliest advanced civilizations (indo-dravidian) even around 6000BC, founders of agriculture and writing, whose heirs were the Mittani (indo-aryans) (whose capital was Arappa) and later the hittites
https://en.wikipedia.org/wiki/Mitanni
Then, the whole area was under Greeks, Romans, then the Hebrew/semitic and then the Arabic.
Coming to our scriptural reference, the descendents of Yayati , who lived west of India were once vedic-aryans, some of them stayed away and wre considered mlechAs/barbaric. All knowledge, philosophy, laws (Smirits) and writing originated in some form or other around central/West India. Read here the descendants of Yayati (that of Chandra Vamshi)
https://en.wikipedia.org/wiki/Yayati
The one branch of lineage of Anu, were the Sibi Chakravarthi, whose descendants were the kadai-ezhu vallals. who later formed the chola dyansties. These may have been the heirs of sumerians. The Solar dyansty, Ishvaku ruled the India from long time, from Central Asia throughout India and the Lunar Dynasties were kept at bay (west Punjab) who might have been the origin of western turkik/arabic cultures