Hello, my name is ***** ***** I will be the immigration attorney helping you today.
If your grandmother has only stayed outside the US for 9 months one time, then yes she should be allowed back into the US this time. She will likely be asked why she was out so long so she should be prepared to explain and have a good excuse. She should also remember always to emphasize that even though she was out for a long time, she considers the US her permanent home.
If she is out of the US for 9 months at a time (or even just more than 6 months) often then it can definitely become a problem because then it will seem like a habit and she can be abused of not actually living in the US.
Good luck to you during this process and I hope this answer has helped you!
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