Nicholas Jackson was arrested at his workplace in Wakefield after the mum pretended to be her daughter and tricked him into sending her his mobile phone number.
The woman was able to use the number to find Jackson's Facebook account to reveal his true identity.
The sex offender was then found in possession of indecent images of children on his mobile phone.
Leeds Crown Court heard the girl's mum became concerned for her daughter's safety in October last after reading messages on her Instagram page from an account called 'Loose Hill Nick'
Michael Collins, prosecuting, said the defendant sent the girl messages describing her as "fit" and asked "how far she would go."
The woman replied to Jackson pretending to be her daughter and discussed meeting him in Wakefield.
Jackson sent his mobile number and a message asking her to delete their conversation.
Mr Collins said the woman was then able to use the number to find Jackson on Facebook.
Jackson had his iPhone seized when he was arrested and taken to a police station.
He refused to tell officers his PIN number for the device.
The phone was later found to contain over 1,000 indecent images of children.
A total of 436 images were at category A - the most serious level of offending.
Some images featured children as young a two being sexually abused.
Jackson, of Linton Road, Eastmoor, Wakefield, pleaded guilty to three offences of making an indecent image of a child and three offences of breach of a sexual harm prevention order.
Jackson was made the subject of the sexual harm prevention order in 2016 when he was convicted of making indecent images of children.
The 46-year-old also has previous convictions for drugs offences, criminal damage and breaching court orders.
Christopher Morton, mitigating, said Jackson committed the offences when he was suffering from depression and anxiety.
Mr Morton said Jackson was an internationally-renowned mountaineer and rock climber.
Jackson was jailed for three years and four months.
Describing the indecent child images, Judge Rodney Jameson QC said: "They are not victimless crimes.
"Real children are raped in order to produce material of this type."