They've urged the individual, who they suspect of stealing the iPhone in Sainsbury’s on the Strand Road in the city on Tuesday, May 22 at around 5 pm, to hand the phone in.
In a statement issued on social media channels, which includes a detailed description of the suspected culprit, the PSNI said images would be published if the woman doesn't do the right thing.
"Do you have a guilty conscience?
"We could go on but we think you get the swing of things. We have clear CCTV image of the female that took it. Save yourself some time and embarrassment of having your picture published in the local papers and possibly on our Facebook page to be seen by thousands!
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"Hand the phone in to Strand Road Enquiry Office quoting reference number 1168 of 22/05/18 and it will find its way back to the rightful owner. Provide your details and I’ll give you a call over the weekend to see how we can deal with it," the PSNI said.