The Alien and the Girl in the Rain — Cheryl Sterling

Curiosity overcomes any moral objections Natalie Cardellini has over meeting an on-line dating match. After all, a cup of coffee and a few minutes of conversation isn't a lifetime commitment.
Natalie doesn't have a lifetime.The diagnosis of an inoperable brain tumor gives her less than six months to live. What harm can come of a glimpse into what-might-have-been?
Lt. Paul Landaeta is on a recruiting mission to Earth, using a computerized dating service to fill his quota for new Slakerian citizens. When a woman matching his date's description leaves without contact, he figures he's been stood up.
The next day he sees her dancing in the rain and is instantly smitten. Can he convince her to leave Earth and join him?
Is Natalie's conversation with him real or a figment of her tumor's cruel sense of humor? Hope is a precious thing to a dying woman. Dare she risk reaching out for it?