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Judging from the below quote was Snape already a double agent when he found out about the meaning of the prophecy?
'Well, Severus? What message does Lord Voldemort have for me?
'No - No message - I'm here on my own account! ... 'I - I come with a warning - no, a request - please -' ... 'What request could a Death Eater make of me?' 'The - the prophecy... the prediction... Trelawney...'
'Ah, yes,' said Dumbledore. 'How much did you relay to Lord Voldemort?'
'Everything - everything I heard!' said Snape. 'That is why - it is for that reason - he thinks it means Lily Evans!'
'The prophecy does not refer to a woman,' said Dumbledore. 'It spoke of a boy born at the end of July -'
'You know what I mean! He thinks it means her son, he is going to hunt her down - kill them all -'
'If she means so much to you,' said Dumbledore, 'surely Lord Voldemort will spare her? Could you not ask for mercy for the mother, in exchange for the son?'
'I have - I have asked him -'
'You disgust me,' said Dumbledore, and Harry had never heard so much contempt in his voice..
This quote seems to imply that Dumbledore was:
- Not suprised to see Snape
- Had given Snape information to relay to Voldemort
However, the general consensus (from what I remember) is that Snape became loyal to Dumbledore only after Lily's death. Given that both sides usually know they are dealing with a double-agent. How did Snape become one?
Option 1: Voldemort sent Snape to find information on Dumbledore.
Option 2: Snape went to Dumbledore to help save Lily.
Option 2 does not seem to fit based on what I take the quote to imply. So, if Option 1 is the case, do we know when it happened?
This question is not a duplicate of Was Severus Snape made a Death Eater before or after he told Voldmort about the Prophecy? because that question is about when Snape became a Death Eater not a double-agent.