My wife did her exam with IOM, including TDAP vaccine, blood tests, and x-rays in Lviv. Then the Russians started shooting missiles at the electrical grid, so she went to Warsaw, got her Johnson's Covid vaccine there, and had the Covid confirmation sent from Warsw to the Doctor that did her exam in Lviv, and that doctor then completed the case. So we started our medical stuff in Ukraine, and finished it in Warsaw... the rule is that doctor that open the case is the one that has to close it, however...
Frankfurt said that they will accept any medical exam completion so long as it's CDC approved. That means you could do the medical in almost any country - as most countries have a list of CDC approved medical examiners.