In the version of this story I know, the husband eventually discovers she's a crane, and when she tries to flee fearing his rejection, he holds onto her tight and tells her he loves her for who she is, not what. (I paraphrase, in the actual story he lists her many good qualities as a wife, and composes a poem to her beauty and grace. Needless to say, she's still skeptical but stays.)

He tells her to get some sleep, and sits with her while she sleeps until sunset the next day. Then scolds her (gently) for ruining her beautiful feathers which grew back in while she slept. At that point she believes he's for real, and says that if she could she'd marry him again.

I think I prefer that version, even if it's probably not authentic.