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We show that, if there exists a diffeomorphism $\\Phi: \\mathcal{C} \\setminus \\overline{B_1(o)} \\rightarrow M \\setminus K$, for some compact $K \\subset M$, such that $\\Phi^{*}J$ is asymptotic to $J_{\\mathcal{C}}$ and $C^{-1} \\omega_{\\mathcal{C}} \\leq \\Phi^{*} \\omega \\leq C \\omega_{\\mathcal{C}}$ for some $C \\geq 1$, then $(M, g)$ is asymptotically conical (AC) with tangent cone at infinity given by $(\\mathcal{C}, d_{g_{\\mathcal{C}}})$. 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We show that, if there exists a diffeomorphism $\\Phi: \\mathcal{C} \\setminus \\overline{B_1(o)} \\rightarrow M \\setminus K$, for some compact $K \\subset M$, such that $\\Phi^{*}J$ is asymptotic to $J_{\\mathcal{C}}$ and $C^{-1} \\omega_{\\mathcal{C}} \\leq \\Phi^{*} \\omega \\leq C \\omega_{\\mathcal{C}}$ for some $C \\geq 1$, then $(M, g)$ is asymptotically conical (AC) with tangent cone at infinity given by $(\\mathcal{C}, d_{g_{\\mathcal{C}}})$. 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