Ibrahim was convicted of apostasy while she was eight months pregnant, and put in prison with her 20-month-old son.
Sources told CNN that her husband, Daniel Wani, a U.S. citizen, was not permitted to be present for the birth.
Ibrahim's lawyer, Mohamed Jar Elnabi, has filed an appeal. The appeals court in Khartoum is expected to issue a ruling next week, once it has received documents used by the lower court to make its ruling. "We will continue checking with the appeals court, but Inshallah (Allah willing) ... the appeals court will reverse the sentence and set her free."
On May 15, Ibrahim was found guilty of apostasy for renouncing the Muslim faith of her father. Ibrahim's father left his family when she was six years old, and Ibrahim was raised a Christian by her mother. She was also convicted of adultery for marrying a non-Muslim man, and sentenced to flogging.
The lower court judge ruled that she will die by hanging.
Notable deaths of 2014 [PHOTOS]
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