Gemma Wilkinson, a former charity worker, took legal action in an attempt to force Anjum to reveal the whereabouts of her daughter Atiya.
Anjum, who represented himself at the latest court hearing, indicated that Atiya was in Pakistan or Iran but said he did not know her exact whereabouts.
Mr Justice Moor said he was sure Anjum was lying.
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The business secretary called the move a 'positive step forward' after the US-imposed tariff sparked fears over jobs in Northern Ireland.
A report published by the Boundary Commission for England details plans to reduce the number of MPs by scrapping 50 constituencies.
The slump will spark scrutiny, especially as statistics show a rise in racially or religiously motivated offences following the EU vote.