If I identify as an eagle, that doesn't make me able to fly.

Sex and gender aren't the same.

"If you were born with an X and a Y chromosome, a dick, and balls, you're male."
***

Yes, that's what I thought as well, but apparently -at least according to the Wikipedia page for "XY sex-determination system"- there are some borderline cases where this is not exactly true (note that they are referred to as "disorders" and produce of a "malfunction"):

"Variations to the sex gene karyotype could include rare disorders such as XX males (often due to translocation of the SRY gene to the X chromosome) or XY gonadal dysgenesis in people who are externally female (due to mutations in the SRY gene)."

"Humans, as well as some other organisms, can have a rare chromosomal arrangement that is contrary to their phenotypic sex; for example, XX males or XY females (see Androgen Insensitivity Syndrome)."

"Clinical phenotypes in these individuals range from a typical male habitus with mild spermatogenic defect or reduced secondary terminal hair, to a full female habitus, despite the presence of a Y-chromosome."

"Androgen Insensitivity Syndrome is divided into three categories that are differentiated by the degree of genital masculinization: (...) external genitalia are those of a typical female; (...) external genitalia are those of a typical male, (...) external genitalia are partially, but not fully, masculinized."

"Management of Androgen Insensitivity Syndrome is currently limited to symptomatic management; no method is currently available to correct the malfunctioning androgen receptor proteins produced by AR gene mutations. Areas of management include sex assignment, genitoplasty, gonadectomy in relation to tumor risk, hormone replacement therapy, genetic counseling, and psychological counseling."

Would she (sorry) be referred to as A Person Who Menstruated Originally But No Longer Does?

I think she would be referred to as an old woman.
Rowling was right but....you can't win an argument by being right these days!

Because insects, as far as we know, do not have fascist societies, in which women’s rights are always the first to go.

That’s what this is really all about: controlling the masses through thought control no matter how idiotic and ridiculous and false and stupid it is. The powers that be use the media to creep closer to a totalitarian world order using propaganda and this gender stuff is the perfect vehicle. Get the population to go along with this gender is whatever you feel like being flapdoodle, and they’re free and clear to get us to go along with ANYTHING.

Reread 1984.

True, but apparently the expression of that Y chromosome can be muted and lead to a more or less female phenotype (see post above about Androgen Insensitivity Syndrome).