The teenager and her infant son were moved from the Al-Hol camp in the north of the country due to "safety concerns around her and her baby", Mr Akunjee said.
Begum, who fled from Bethnal Green in east London to join Islamic State as a 15-year-old, recently said she regretted speaking to the media.
The 19-year-old, who gave birth days after her a journalist tracked her down to a refugee camp in northeastern Syria, said she wished she had kept a low profile.
It was reported that Begum had received death threats since speaking out about her plight of being stripped of her British citizenship, blocking her return to the UK.
The mother and her baby are said to have since been moved to another camp.
Akunjee said at the time it was his understanding that his client had been moved from al-Hol due to safety concerns around her and her baby after "she and her child had been threatened by others" at the camp.
Last month, the development comes after British officials ruled out any effort inside Syria to extract Begum and her child.
Sajid Javid, Home Secretary, stripped her of her British citizenship in an effort to stop her returning.
Begum's family have pleaded for the mother and her child to be allowed to come back to Britain.
They say the teenager should face justice if she is found to have broken the law by travelling to Syria.
Begum defends Manchester Arena bombing
The teenager, who gave birth to a baby boy in mid-February, appeared to defend the Manchester Arena bombing as tit-for-tat retaliation for air strikes in Syria.
In an interview with the BBC, she said the deaths of 22 innocent people in the terrorist attack at an Ariana Grande concert in 2017 were akin to the "women and children" being bombed in Isis territory in Baghuz.
She told the broadcaster: "I do feel that it's wrong that innocent people did get killed. It's one thing to kill a soldier that is fighting you, it's self-defence, but to kill the people like women and children...
"Just people like the women and children in Baghuz that are being killed right now unjustly, the bombings. It's a two-way thing really.
"Because women and children are being killed back in the Islamic State right now and it's kind of retaliation. Like, their justification was that it was retaliation so I thought 'OK, that is a fair justification'."
She was partly inspired by videos of fighters beheading hostages and partly by other propaganda films showing the "good life" Isis could offer.
"Show me some sympathy", says Isis bride after giving birth
The British schoolgirl who ran away to join Isis appealed for public sympathy following the birth of her son.
In an interview with Sky News recorded at the Kurdish-controlled camp to which she fled from the last pocket of Isis-controlled territory, Begum said there was "no evidence" she had done anything wrong and she could not see "any reason" why her child should be taken from her when she had simply been living as a housewife.
Speaking just hours after giving birth, her baby at her side, she said she had no regrets about fleeing the family home in Bethnal Green, east London, to support Isis, claiming the experience had made her "stronger, tougher".
She said she could see a future for herself and her son, whom she has named Jarah after one of the two children she lost to malnutrition and disease in the last three months, "if the UK are willing to take me back and help me start a new life again and try and move on from everything that's happened in the last four years".
She added: "I wouldn't have found someone like my husband [Yago Riedijk, 26, a Muslim convert from the Netherlands] in the UK. I had my kids, I had a good time there."
Her other children, Jarah and Surayah, a daughter, died aged 18 months and nine months. Asked how she felt about the debate over whether she should be allowed to return home, Begum said: "I feel a lot of people should have sympathy for me, for everything I've been through.
"I didn't know what I was getting into when I left, I just was hoping that maybe for the sake of me and my child they let me come back.
"I can't live in this camp forever. It's not really possible."
In the interview, Begum apologised for the first time to her family for running away, and said that though she knew it was "like a big slap in the face" for her to ask after she had previously rejected their calls for her to return, "I really need their help".
Begum was "OK" with Isis beheadings
The Isis bride said in February she was attracted to Isis by videos that she had seen online, which she said showed "how they'll take care of you".
She said she knew that the group carried out beheadings, but that she "was OK with it at first. I started becoming religious just before I left and from what I heard Islamically that is all allowed".
"At first it was nice," she said of life in the so-called Islamic State. "It was how they showed it in the videos, you know, you come, make a family together, but then things got harder.
"We had to keep moving and moving and moving. The situation got fraught." Begum acknowledged that it would be "really hard" to be rehabilitated after everything she had been through.
"I'm still in that mentality of planes over my head, emergency backpacks, starving... it would be a big shock to go back to the UK and start again," she said.
This article originally appeared on the Daily Telegraph.
