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The ancestor property was first defined by Hart and Rowley in \\cite{hart2025noteinvolutionprefixescoxeter} where they conjectured that all non-identity elements in a finite Coxeter system have the ancestor property. 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Let $ [1,w] := \\{ x\\in W \\mid x \\leq_{R} w \\} $ where $ \\leq_{R}$ denotes the weak right order of $ (W,S)$. The element $ w$ is said to have the \\emph{ancestor property} if there is a unique non-trivial involution of maximal length in the set $ [1,w]$. The ancestor property was first defined by Hart and Rowley in \\cite{hart2025noteinvolutionprefixescoxeter} where they conjectured that all non-identity elements in a finite Coxeter system have the ancestor property. 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