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For some reason, there was a catastrophic shortage of money in this mission.
That's definitely true.
You will be able to convert cities when all four have been captured.
But I managed to convert them when only 3 out of 4 were captured. When I converted one of the cities, a disgruntled orc immediately appeared and started interfering with the fight against the monsters, so I replayed it a bit and started converting after capturing the 4th castle. :)