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Using Furusawa's integral representation for $\\GSp_4\\times\\GL_2$ combined with a pullback formula involving the unitary group $\\GU(3,3)$, we prove that the $L$-functions $L(s,\\pi\\times\\tau)$ are \"nice\". The converse theorem of Cogdell and Piatetski-Shapiro then implies that such representations $\\pi$ have a functorial lifting to a cuspidal representation of $\\GL_4(\\A)$. 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Using Furusawa's integral representation for $\\GSp_4\\times\\GL_2$ combined with a pullback formula involving the unitary group $\\GU(3,3)$, we prove that the $L$-functions $L(s,\\pi\\times\\tau)$ are \"nice\". The converse theorem of Cogdell and Piatetski-Shapiro then implies that such representations $\\pi$ have a functorial lifting to a cuspidal representation of $\\GL_4(\\A)$. 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