KYIV—The Ukrainian police video shows a doctor seated at his desk while a masked officer counts bundles of cash found stashed in the office: $12,000 worth in total. The televised raid this week on a doctor’s surgery in the Khmelnytsky region is one of hundreds of criminal investigations publicised by the authorities in a clampdown on a flourishing black market in forged vaccine and COVID-19 test documents. After a lull in the summer, Ukraine is experiencing some of the highest death rates from COVID-19 in the world. One of Europe’s poorest countries, Ukraine lagged behind its neighbours in procuring vaccines earlier this year. Now, as in other former communist states in eastern Europe, it is struggling to persuade a sceptical population to take them. Only around 7 million Ukrainians out of a population of 41 million are fully jabbed against COVID-19 and surveys suggest around half of adults do not …