DNIPRO, Ukraine/MALMO, Sweden -- In their quest to bring Ukraine its second Eurovision crown in three years, singer-songwriters Alyona Alyona and Jerry Heil are performing a song about the strength of women. They're also on a mission that puts that message to the test: raising the equivalent of over $250,000 to restore a war-damaged school in a southern region ravaged by Russian attacks.

"We want...