Wegener, a Danish-born artist began cross-dressing when his wife Gerda—also an artist—asked him to model for her when her own model failed to show up. He discovered he enjoyed the soft femininity of women's clothing and dressing in drag soon became part of his life. As for Gerda, whose erotic lesbian watercolors are still readily available online, she found herself more attracted to her husband when dressed as Lili. Beginning in 1930, in Germany, Einar underwent a series of experimental surgeries to make his transformation from man to woman complete.
Ebershoff's book is actually a novel inspired by Einar Wegener's story, so I'm not clear whether the film follows suit or whether it attempts to tell the true story. That true story was told in a memoir called Man Into Woman. While the couple remained friends they eventually parted and had other relationships. Gerda remarried and Lili fell in love with a young painter. Even though she was 48 years old, Lili hoped to become a mother, and went in for one last surgery—the transplantation of a uterus. Her body rejected the organ, and tragically Lili died two days later.
The movie also stars Alicia Vikander as Wegener's wife Gerda Gottlieb, along with Amber Heard and Matthias Schoenaerts. Tom Hooper—who directed Redmayne in Les Miz—helms the picture, from a screenplay by Lucinda Coxon. Look for The Danish Girls in theaters November 27th!
Thanks @bespokeredmayne for the update.
Sources: The Coil House, The Wrap, The Daily Mail