The woman's mobile was one of about 40 devices worth thousands of pounds taken during two overnight raids at the Talk Time store on Ecclesall Road.
Shop owners have now released three CCTV videos allegedly showing a man breaking into the store at midnight on Friday, August 25, before returning at 4am to carry out his second raid of the night.
Shop co-owner Shazad Ahmed, aged 40, told how the mum whose phone was taken did not want to be identified, but added: "She is distraught, very upset.
"Her young son died last year and we are concerned the pictures have now been lost.
"We are desperate to get the phones back, and this one in particular.
"We are trying to establish ourselves as a business and can't believe someone would do this."
The store specialises in both selling phones and repairing damaged ones.
The burglar took two displays of new mobiles, including expensive iPhones and iPads, and a box of repaired customers' phones that were awaiting collection.
Mr Ahmed said the items taken are worth about £2000 and the raider also took £2000 from the till.
He added that he broke in by smashing in a window upstairs and removing metal bars.
The raider also wore gloves so police have not managed to identify any fingerprints yet.
CCTV footage shows a white man with short hair wearing a white t-shirt carrying out the raid.
Mr Ahmed urged anyone who recognises the man to contact police.
He said: "Please get in touch if you know this man, his face is very clear on some of the footage.
"The main thing we want is to get the stock and the money back."
South Yorkshire Police has not yet released any details about the incident. The force has been contacted for comment and we are awaiting a reply.