Dear Prof. R R:

You wrote:
> Could you please tell me if the sentence below is correct English. If it
> is
> correct, what does it mean? Is it in common use?
>
> “Either of the girls has her own camera.”
>
> Thank you.
>
This is awkward and ambiguous. Do you mean “both of the girls” or do you mean “either one or the other of the girls”? Say what you mean.

This is not a common use because it is ambiguous. I cannot imagine anyone saying it. “Neither of the girls” is commonly heard because that is a negative and that means that no girl has a camera.