When Kimiyo Hoshi was first introduced way back in Crisis on Infinite Earths, she was a doctor, a scientist, and a single mother with two children, and she lived in Japan. After a long stint with the JLA she eventually retired from the hero biz to spend more time with her children. In Infinite Crisis she joined the fight, protecting her homeland (still Japan) from attack.
In Green Arrow in a story supposedly taking place after IC but published some six months before, Kimiyo is a management executive in America. Her powers are taken away and she is left dying. Now in Birds of Prey we find her alive and well, apparently with powers, and working as a scientist in Japan.
So what exactly happened here? Here are my theories:
1) Superboy Prime's reality punching activities created an alternate universe in which Kimiyo's entire backstory and geographical location were different. This alternate universe collapsed before anybody noticed it other then Green Arrow, who didn't care enough to check whether Kimiyo was still alive at the end of the story.
2) It was a clone.
3) Dream? Hoax? Imaginary story? I'm running out of ways to explain away Judd Winick's lazy writing and his editor's negligence.
In fact my best guess is that the blanks will be filled in during 52. Either that or everyone is going to pretend the Green Arrow story never happened.