According to the Vishnu Purana the original Veda was divided into four parts, and further fragmented into numerous shakhas, by Vishnu in the form of Vyasa, in the Dvapara Yuga; the Vayu Purana recounts a similar division by Vyasa, at the urging of Brahma. The Bhagavata Purana traces the origin of the primeval Veda to the syllable aum, and says that it was divided into four at the start of Dvapara Yuga, because men had declined in age, virtue and understanding.
However, if we consider the order of evolution of Vedas, Mahabharata, Srimad Ramayana, etc, we can understand that Vedas were followed by Srimad Ramayana. And, after a long period Mahabharata came into existence.
So if we go by these stories, the Vedas should have been remained undivided in the Ramayana era. If we read Srimad Ramayana carefully, we will find that Vedas were already divided into 3 parts by the time Sri Rama came into existence.
1) Sri Hanuma approaches, at the behest of Sugreeva, Sri Rama and Lakshmana to know the intentions of those two by their conduct, by their semblance, and by their conversation.
After listening to him, Sri Rama expresses his opinion on Sri Hanuma to Lakshmana as follows:
न अन् ऋग्वेद विनीतस्य न अ--यजुर्वेद धारिणः | न अ--साम वेद विदुषः शक्यम् एवम् विभाषितुम् ||
(Kishkinda Kanda 3rd Sarga 28th Sloka)
"Nay...the non-knower of Rig Veda, or the non-rememberer of Yajur Veda, or the non-scholar of Saama Veda... can possibly, or truly speak this way..."
Here, Sri Rama was saying that Sri Hanuma was well versed in Rig, Yajur, Saama Vedas. So by that time Vedas might have already been divided into 3 parts only but not 4 parts.
2) While describing the characteristics and bodily signs of Sri Rama to Sita, Sri Hanuma says as follows:
यजुः वेद विनीतः च वेदविद्भिः सुपूजितः | धनुः वेदे च वेदे च वेद अन्गेषु च निष्ठितः || (Sundara Kanda 35th Sarga 14th Sloka)
"He got trained in Yajurveda, the sacrificial Veda. He is highly honoured by those well-versed in Vedas. He is skilled in Dhanurveda, the science of archery, other Vedas and the six limbs of Vedangas."
Sri Rama was trained in Yajurveda. So Vedas were divided in Srimad Ramayana era itself.
Then why this division of Vedas was attributed to Sage Vyas?