My mother received an unfounded diagnosis from her doctor saying she will lose movement in her hand in the future.
ご質問ありがとうございます。
この場合、「unfounded」という英単語を使いたいなら下記、の英文通りになります。
My mother received an unfounded [diagnosis](https://eikaiwa.dmm.com/uknow/questions/37053/) from her doctor saying she will lose movement in her hand in the future.
ご参考になれば幸いです。