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In this paper we explicitly express in terms of the scale function and the L\\'{e}vy measure of $X$ the law of the sextuple of the first-passage time of $Y$ over the level $a>0$, the time $\\bar{G}_{\\tau_a}$ of the last supremum of $X$ prior to $\\tau_a$, the infimum $\\unl X_{\\tau_a}$ and supremum $\\ovl X_{\\tau_a}$ of $X$ at $\\tau_a$ and the undershoot $a - Y_{\\tau_a-}$ and overshoot $Y_{\\tau_a}-a$ of $Y$ at $\\tau_a$. 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