The children's charity is calling for new laws to force social media firms to be more proactive in tackling online child abuse.
She took the messages to Pauline after being asked her bra size and told the male was 'thinking about playing with myself'.
The male's account remained active after Pauline was told he had not breached the site's community guidelines but was taken down after Instagram was contacted by The Sun Online.
It comes after the NSPCC found the number of child grooming cases on Instagram tripled in the UK to 428 last year.
Molly - who went to Hatch End High School in Harrow, Middlesex - had started viewing the disturbing posts without her family's knowledge.
Ian told the BBC: "I have no doubt that Instagram helped kill my daughter.