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We show that there exists a particularly nice Springer isomorphism for $G$ which restricts to a certain canonical isomorphism $\\text{Lie}(U_P) \\xrightarrow{\\sim} U_P$ defined by J.-P. Serre. This answers a question raised both by G. McNinch in \\cite{M2}, and by J. Carlson \\textit{et. al} in \\cite{CLN}. 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