The incident took place on Ladycross Road, Hythe, between 3pm and 8.30pm on Monday, July 21.
The suspect reportedly visited a property to buy a mobile phone but swapped the device with another box containing stock cubes.
No money was exchanged for the phone.
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A spokesperson for Hampshire police said: “We believe the man in these images can help us with our investigation and would urge him, or anyone who knows his identity, to get in touch with us.”
The police are also appealing for anyone who witnessed the incident, noticed any suspicious activity in the area at the time, or has any relevant footage, to contact them.
Information can be reported by calling 101, online via the Hampshire & Isle of Wight Constabulary website, quoting incident number 44250332146.
