Sree Vidya Ramayanam is a version of Ramayana (the story of Lord Rama) that is based out of Devi Sree Lalitha. This says, Lalitha rules the world and all the happenings in Ramayana are also by the orders of Lalitha.
The story of Ramayana as per Srividya ramayanam is as follows.
This starts with the conversation between Agastya and Hayagreeva. Agastya asks Hayagreeva to explain him the Guhya thathvam (secret philosophy) of Brahmmanda purana. Hayagreeva explains it to Agastya as follows.
Once Indra wanted to test the lovely couple (Agalya - Gauthama). So Indra disguised himself as a cock and went to Gauthama's ashram before the day dawned. By making sound like a cock, Indra tricked Gauthama and the latter went out to the river bank for having bath thinking that the day had dawned. At the ashram Agalya was left alone. Indra appeared as Gauthama and tried to misbehave with Agalya. Agalya being a pathi vrathai (one who never thinks of a man other than her husband) and a Devi bhakthai (devotee), found out the intention that Indra was having in his mind and prayed to Devi to save her and make Indra realise his mistake.
Initially before starting for execution of this task, Indra (also a devi devotee) prayed to Devi to protect him in case of any trouble. So after listening to Agalya's plea to save her, Devi turned Agalya into a stone. Now neither Indra nor Agalya would get a bad name.
Indra realised his mistake on seeing Agalya turning into a stone. Gauthama on seeing Indra at his ashram and agalya turned into a stone, judged what could have happened with the prowess of his tapas (meditation).
Origin of Sree vidya ramayanam
To kill the asuras Lalitha originated from the "chith agni kundam" and after killing asuras she married Lord Kameshwara (form of Lord shiva, adorned with jewels). Every body was happy. but Gauthama was still thinking of Agalya. On seeing this, Lalitha announced that everyone including herself will suffer for not helping Agalya at the time of her difficulty in the Ramayana time.
So she said "My form Narayanee will be born as Rama and Narayanan will be born as Lakshman. Form of Parameswara and Brahmma will be born as Bharatha and Chatruguna.
Indra who troubled Agalya is similar to monkey. So he was borne as Sugreeva, the monkey king.
Like Gowthama who suffered a lot from being separated from his wife, Rama, Sugreeva will also need to pay their debt. (Rama and sita wil part and similarly sugreeva and Tara)
Relation to Ramayana
Kausalya, Kaikeyi and Sumitra, wives of King Dasaratha of Ayodhya were ardent devotees of Sree Lalitha, Parameswara and Brahmma,Vishnu respectively. They prayed to their favourite deities and got child(ren) of their choice. Kausalya gave birth to Rama (Devi's form), Kaikeyi to Bharatha (Parameswara's form) and sumitra gave birth to Lakshmana (Vishnu's form) and Chathruguna (Brahmma's form).
The rest are similar to Ramayana by Valmiki. But all happenings are centered at Devi's command.
Many versions of Ramayana exists. We cant say this is the right one or so. All are aimed at increasing one's faith towards God. If we take the situation where all including Devi herself are suffering the punishment for not helping Agalya, we can conclude that even God need to repay his debts. This is the wonderful principle of equality.
This Sree vidya ramayana, enforces optimism. If one thinks positively
1. All that happened will seem to be good
2. All that is happening will be good.
3. All that will happen will also be good.