The police officers who were called to the incident decided to donate £200 to the family from the force's Tuck Shop.
Sergeant Richard Markham, from West Midlands Police, which are investigating the burglary, said:
"Stealing children's Christmas presents is such a heartless and callous thing for anyone to do. We wanted to try and put a smile back on their faces for Christmas.
"We're determined to track down whoever did this and would urge anyone with information that could help to come forward.
"If you know who is responsible please do the decent thing and call us before those responsible cause heartache like this for another family."
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Another warm day with patchy cloud and sunny spells.
The court heard Peter George Bell diverted funds from the company client account to finance a lavish lifestyle.
The shoes date back to 1690 and are thought to be worth hundreds of pounds.