Can a 2002 Buick century transmission work properly in a 2003 Buick?

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Transmission quit pulling. Did a little research said you have to look at Id sticker on trunk lid to see if it has matching numbers like torque converter transmission wire harness. And also matching pro. Can anyone confirm this thanks Frustrated and confused in Batesville ms! Can a 2002 Buick century work in a 2003 Buick century?