Hodu L'Hashem ki Tov—Give thanks to God for He is Good!
She still needs additional oxygen to breathe, but her lungs are getting stronger all the time.
However (excerpted from the original email message):
She still has a long way to go.
The doctors said that she is alive is a miracle and only due to the prayers and Tehillim [Psalms].
The family is very grateful for everyone's davening and Tehillim.
Please continue to daven and say Tehillim for her.
You and everyone else who has been davening for her & her baby, or doing good deeds in their merit.
Remember, she initially gave birth unconscious & was described as "fighting for her life."
And within less than a month, she went from "fighting for her life" to being awake, breathing with increasing improvement, and able to hold her baby!
Apparently, the doctors initially did not hold much hope for her, but prayers & good deeds saved the day.
Let's take this as chizuk (encouragement) to continue davening for Chava Leah bat Esther (and anyone else in need) with the knowledge that our prayers & deeds really are precious to Hashem.
And He's accepting & fulfilling the prayers.