In Kottwitz's paper "Stable trace formula: cuspidal tempered terms", it is said that if $$1 \rightarrow G_1 \rightarrow G_2 \rightarrow G_3 \rightarrow 1$$ is an exact sequence of connected reductive groups over some number field $F$, then the sequence $$ 1 \rightarrow Z(\widehat{G_3}) \rightarrow Z(\widehat{G_2}) \rightarrow Z(\widehat{G_1}) \rightarrow 1 $$ is exact too (the hats stand for complex dual groups and the $Z$ for their center).

Can anybody give me a reference for this statement?