Begum was 15 when she and two friends left London to marry IS fighters in Syria in 2015, at a time when the group's online recruitment program lured many impressionable young people to its self-proclaimed caliphate.
She resurfaced heavily-pregnant at the Syrian refugee camp last month and spoke of her desire to return to the United Kingdom, as the self-styled caliphate collapsed.
In an interview with the BBC after the birth of Jarrah, she said she did not regret travelling to Syria - although she added that she did not agree with everything the IS group had done.
Home Secretary Sajid Javid confirmed Begum's son was a British citizen but said it would be "incredibly difficult" to facilitate the return of a child from Syria.
Shamima Begum carries the burden of her actions but her newborn baby carried no burden whatsoever. But he later deleted the tweet without explanation, and shortly after confirmed the baby's death.
Her Dutch jihadi husband Yago Riedijk, who is in a Kurdish-run detention centre, said last week he wanted to return to the Netherlands with Ms Begum and their son.
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Whilst the Home Office can not make her stateless, they are able to revoke her citizenship if she is found to have acted "in a manner which is seriously prejudicial to the vital interests of the U" and if he claims to have "reasonable grounds for believing that the person is able, under the law of a country or territory outside the United Kingdom, to become a national of such a country or territory".
She also said that she never sought to be an IS "poster girl" and simply wished to raise her child quietly in the UK.
Mr Javid has insisted Begum will not be left "stateless" - something which is banned under worldwide law - after her United Kingdom citizenship was stripped, amid speculation that she is a dual British-Bangladeshi national.
Earlier this week, Mr Akunjee tweeted a screenshot of the reply that they had received from the Home Office.
Home Secretary Said Avid said he did not know if the baby, a British citizen, had died.
The FRO is obliged to consider requests for consular assistance, the letter added.