KYIV, Ukraine—In 2020, Vitaliy Yatsenko went to pick up a parcel containing illegal amphetamines from a Kyiv post office and was met by 10 policemen and detained. This week he will cut short his five-year prison sentence to join Ukraine’s stretched armed forces. In a sign of the Ukrainian military’s desperate need for fresh troops, Kyiv is taking a leaf out of Russia’s playbook by recruiting inmates from prisons to serve in its armed forces. The government says that 4,656 convicts have already applied for the program in which prisoners will have to serve till the end of the war...