Irram, whose first birthday was on 16 December, was given back to Nasreen Siddiq, 23, in a London hospital. She had been taken from near her home in Sparkbrook, Birmingham, in September. She was found in a push chair in the call box in Southall, west London, at 6.40pm on Friday.
As Ms Siddiq posed for pictures cuddling her baby, police from Scotland Yard and the West Midlands were liaising to find who abandoned the child.
A police spokesman said it was evident that no harm was meant to come to the baby, who was found in a well-lit telephone box and had been left for less than an hour.
Police believe she had been passed off as a boy - she had been dressed like a boy and had close-cropped hair. Fourteen weeks of 'pure hell' ended for Ms Siddiq, who is separated from her husband, as she watched the news on television. An item about an abandoned child was accompanied by a picture of Irram.
'It was my little baby and I just started crying,' she said. She phoned Southall police who asked her to travel south to see the baby. Arriving with her parents and cousin, she was taken to Ealing Hospital where nurses had called the baby Sarah.
Her baby had not recognised her at first, she said. 'It has been some time since she has seen me. It is only natural she did not recognise me but she has got used to me now. I feel wonderful.'
Once medical tests are over, mother and daughter will return home to a pile of unopened birthday and Christmas presents.
Three men have been in custody since before Christmas charged with kidnap and blackmail in relation to the baby's disappearance.
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