District Judge David Taylor said "any honest person" would have reported the winnings within a short time of receiving them and said he was satisfied Caroline Banana's behaviour did "amount to a deliberate cover up".
He pointed out Banana had only admitted her guilt on the eve of her trial last week, giving her "minimum credit" for that guilty plea.
Mr Taylor, sitting at North Staffordshire Magistrates' Court, ordered Banana to carry out a 12 month unpaid work order, with supervision by the probation service.
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A band of persistent, occasionally heavy rain moves eastwards over the region.
Winds increasing further on Monday morning with a persistent band of rain sinking south across the area by midday.
Thousands of runners took part in the Great Birmingham 10K. The 6.2mile event went around the city, ending on Broad Street.