A Suzuki Vitara was the target of the early hours break-in on January 21, with the incident reported to have taken place around 3am in Dingle Way.
These cards were then used to purchase several items at Smart Stop and Brothers Convenience Store, both on Fratton Road, Portsmouth, at about 6.45am the same day.
As part of their investigation, officers are now issuing an image of a man they would like to speak to.
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Do you know him? (Image: Hampshire Constabulary) A spokesperson for Hampshire Constabulary said: “We would like to speak to the man in this image and anyone who knows him.
“If you have any information regarding this incident, please call 101 quoting reference 44250029928.”