Caroline Banana, of Bentilee, further admitted making a false representation on an Income Support application form by not declaring she was owed her TV gameshow winnings, in April 2011.
She also pleaded guilty to wrongly claiming free school meals for three children.
She now has 12 months to settle her over-payments in full.
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Des Coleman has the West Midlands weather forecast.
Des Coleman has the weather forecast for the East Midlands
“Amy was a young woman with her life ahead of her. Sadly, Amy’s history is similar to many domestic abuse cases".