Gary Plant (31) was jailed for 32 months in 2014 after he sent a 15-year-old girl a Facebook message asking to meet for sex.
Burnley magistrates were told Plant was said to have started a sexual relationship with the woman after they met in a Colne pub and stayed at her house when her children were there. She told police she felt sick and angry when she found out his background.
Plant could now be facing jail after admitting failing to comply with the notification requirements of the register, between September 1st last year and March 21st this year.
The defendant, of Romney Street, Nelson, will be sentenced next month. The justices told him they believed it was a deliberate failure to comply with the register and was over a long period of time.
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Mr Andrew Robinson (prosecuting) said in 2014, Plant was convicted of facilitating the commission of a child sex offence. He was placed on the Sex Offenders' Register and given a five-year Sexual Offences Prevention Order. The defendant was supposed to register any other name he was using to the police within three days.
He met a woman in a pub last September, calling himself Gary Crossley.
Mr Robinson said: "On March 2nd, the woman received a text message from the defendant saying he was on the Sex Offenders' Register and his name was Gary Plant."
Mr Kamran Yousaf (defending) said Plant told the woman within a month of meeting what his real name was and that he was on the Sex Offenders' Register.
He added: "He did have sex with her on one occasion and after that it was friendship. He accepts going to her house, but not as much as the prosecution say."