It really depends on how the name is written in Japanese.
The most common form of Nuiko that I can find is 縫子, composed of 縫
(nui) meaning "embroidery, sewing" and 子
(ko), a common feminine suffix meaning "child." Other forms that I can find include ぬい子/ヌイ子 (ぬい/ヌイ being hirakana/katakana renditions of Nui), 布衣子, composed of 布
(nu), shortened from
nuno meaning "cloth," and 衣
(i) meaning "clothing," and 縫衣子.
I'm guessing 縫子 or ぬい子/ヌイ子 might be how her deceased grandmother's name was written, but I wouldn't be 100% sure on that until you can be able to find out for yourself.
Best wishes for her upcoming birthday and good luck.
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