Putin does not trust anyone. So he hired a guard of Kadyrov. And as payment for the loyalty to him is given to Moscow. Putin lost the Chechen war.
Perhaps you should read the history books again? The first Chechen war ended in stalemate, with heavy casualties to both the sides. The Russian troops had to pull out of Grozny and the other Chechen cities. But the second Chechen war resulted in the destruction of the rebels. Most of them were killed, and the remaining are now living as refugees in the US, where they are contributing to the American-style nation building (such as Tamerlan Tsarnaev and Dzhokhar Tsarnaev).
This is the official result. But there is no official result of the second Chechen war. Kadyrov who killed Russian soldiers received the star of hero of Russia has a lot of money, acting like the winner and Russia is building a formidable. Who won the war?