Welcome back and nice to hear from you again!
Regarding your question, however, I am afraid that the fact that your child was born in Berlin will not promote the chances for a relocation/transfer (Umverteilung) from Sachsen to Berlin. Instead, the application for the "Umverteilung" may be approved in the context of work/training reasons or for a family reunification.
I hope these information are useful for you and please don't hesitate to get back to us with any further questions.
All the best,