One of the victims was injured grandmother Pauline Healey, who's granddaughter sadly died in the attack.
Police arrested Parker, who has previous convictions for burglary, on Tuesday after he failed to appear at Manchester Crown Court.
Parker faced eight counts in total but denied five offences, including attempting to steal a coat and a bag and using Healey's Yorkshire Bank card at Tesco on Deansgate in Manchester and to buy a public transport ticket.
Prosecutors will not pursue a number of other charges following the guilty pleas.
"I was really shellshocked by it all". The judge told Parker a custodial sentence was "most likely".
Parker claimed he cradled a dying woman in his arms after the blast and wrapped a T-shirt around an injured girl - when in reality he had looted a phone from a teenage girl. Parker was reportedly unable to leave his cell while in custody due to death threats from other inmates.
In a statement on the GoFundMe page, Mr Johns said: "I would like to extend my sympathies to his victims that night and also apologise to them for any distress this campaign may have caused them whilst they continue to recover and grieve".
The prosecutor argued that although he offered "limited help" to the injured, he took advantage of the conditions for committing theft.
Salman Abedi's suicide bombing killed 22 and left scores injured on May 22 a year ago.
Her granddaughter Sorrell, a pupil at Allerton High School in Leeds, was hoping to be an architect and wanted to study at Columbia University in NY. The explosion happened as people were leaving an Ariana Grande concert.
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