A woman handed cash to bogus couriers in the car park of the McDonald's in Sudbury.
The incident happened outside the restaurant on the Chilton industrial estate on two occasions.
The first incident happened at about 12.45pm on Tuesday, June 7, with the second at about 3.30pm the following day.
Suffolk police said the woman was from Long Melford.
Anyone who witnessed either of these incidents or who has dashcam footage is asked to contact Suffolk police, quoting crime reference number 37/35680/22.
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