I have imprisoned Prince Yuri Boryatinsky and have also captured the whole world in the game Mount and Blade - With Fire and Sword. How do I find him to continue the quest of the secret of the black mace?
To answer your questions at a basic level: If you've captured Prince Yuri then he should be in your prisoners (in the party screen) or he will be in the dungeon of whatever town/city that you left him in. If you speak to any lord in his faction they might be able to tell you where he is.
However, speaking to him as a prisoner may not trigger the dialogue you need to continue the quest. You could release him and then talk to him when he re-emerges as a free lord...but you've already conquered the whole map so this might not happen. Have you received a notification saying the Muscovite Tsardom has been wiped out?
Even if you do manage to trigger Prince Yuri's continuation of the quest I suspect that you will probably have problems completing the whole thing. The Secret of the Black Mace quest is notoriously buggy and by conquering the whole world you've jumped ahead of the story line.