Character Analysis
Greta's Got It
Greta isn't like most wives. After all, most wives don't have husbands who want to be wives, but even if they did, most wives (the ones who start the relationships as wives) probably wouldn't be as supportive as Greta is of Einar when he wants to become Lili.
One reason Greta is supportive is a selfish one: Lili inspires Greta. Lili is a living work of art, and a true artist knows a work of art when she sees it. The first line of the book is "His wife knew first" (1.1); Greta sees the potential for Lili within Einar before Einar even does.
Some might go so far as to say that Greta deserves credit for creating Lili herself. It's Greta who puts the dress on Einar; it's Greta who names her Lili; it's Greta who encourages Lili to come out. And it's Greta who finds Professor Bolk to perform the surgery on Einar, helping alter his body so he can better live as Lili all the time.
Another reason Greta is so supportive, however, is less selfish: Greta knows what it feels like to desperately want her own identity. Both she and Einar want to be their own person. Greta, who grew up in California, feels stifled, so she moves to Denmark, a country smaller than the state of California: "Greta agreed that it didn't make sense, but this was how she felt" (4.3). She needed to get out, to find new space to be herself in.
At the time, it doesn't make sense for a man to want to be a woman—there aren't the social understandings of gender and trans identities that we have today—but Greta is able to identify with her husband because she has felt similarly, albeit without the need to shift her gender presentation. Taking a ship across the ocean isn't in the same league as sex reassignment surgery, but the emotional drive underlying these journeys is similar.
We Pronounce You Husband and Wife (and Wife)
Einar and Greta are more similar than you might think. Einar/Lili knows what they want. Einar wants to be a woman (we're not saying that process is simple, but that he has a clear goal), and Lili wants a husband. Greta seems confused and conflicted internally, but all she really wants is to support her husband. She, too, has a clear goal, then, and it's the same as Einar's: Lili's happiness.
However, the goal—and Greta—become confused and lost when her husband disappears, fully replaced by Lili. This is when Greta realizes that she is living in a (way) less-creepy version of Invasion of the Body Snatchers. She is living with a woman who used to be her husband. Adding to Greta's difficulty, Lili should have her husband's memories but she claims not to. It's amazing that Greta is able to handle such an unusual situation with calm, but that's Greta for you.
Just because she doesn't flip her lip, though, doesn't mean that Greta just keeps on keeping on. Instead Greta gives up, something she'd never have done while married to Einar. Of course, Greta never dreamed her husband would become a woman either, so yeah, things change. But if you examine their marriage, you'll see that it's always Greta who will do anything for Einar, not the other way around. Even Greta has her limits, though, and much as she encourages Einar to live as Lili, when he finally truly does, Greta finds there's little for her in their marriage any longer.
When Lili is to be married, Greta finally decides to live life for herself… Well, not entirely. Greta takes on Einar's abandoned memories. She keeps his paintings, and she even starts painting landscapes of her own (as he once did), though she paints landscapes of her childhood. Greta always valued her marriage, so in the end, she becomes a blend of herself and her husband. She even starts a romance with Einar's childhood friend, Hans, whom Einar always had a bit of a crush on. It isn't quite the same as Greta transitioning to becoming a man, but she does incorporate many of Einar's attributes into her new identity.
Greta's Timeline