When Ali Cobby Eckermann met her biological mother for the first time at age 34, she did not think her life could be enlarged further, she said. Four years later, in 2001, Ms. Cobby Eckermann was reunited with her son, then 18, who had been taken from her at birth.

The trauma of being removed from her birth mother and being separated from her son as part of Australia’s so-called stolen generation of Indigenous Australian children has rippled through decades of her life. It led to abuse and isolation, alcohol and drugs, and a profound sense of grief.

It also led to poetry. After leaving rehab and recovering from her lowest point, Ms. Cobby Eckermann, now 54, started writing as a way to heal and to tell her family’s story. In the coming week, she will be at Yale University to receive a Windham-Campbell writing prize, one of eight recipients this year selected from around the world. The secretive award, which accepts confidential nominations and does not inform writers they are being considered, comes with a prize of $165,000.

“Coming out of Maralinga, South Australia, my family always knew their story was important,” Ms. Cobby Eckermann said. But the recognition the prize has brought has been overwhelming, she said in an interview. It is only in recent weeks that she has been able to say, without crying, that she is the first Aboriginal Australian to receive the prize.