We present new integral field spectroscopy of the gravitationally lensed broad absorption line (BAL) quasar H1413+117, covering the ultraviolet to visible rest-frame spectral range. We observe strong microlensing signatures in lensed image D, and we use this microlensing to simultaneously constrain both the broad emission and broad absorption line gas. By modeling the lens system over the range of probable lensing galaxy redshifts and using on a new argument based on the wavelength-independence of the broad line lensing magnifications, we determine that there is no significant broad line emission from smaller than ~20 light days. We also perform spectral decomposition to derive the intrinsic broad emission line (BEL) and continuum spectrum, subject to BAL absorption. We also reconstruct the intrinsic BAL absorption profile, whose features allow us to constrain outflow kinematics in the context of a disk-wind model. We find a very sharp, blueshifted onset of absorption of 1,500 km/s in both C IV and N V that may correspond to an inner edge of a disk-winds radial outflow. The lower ionization Si IV and Al III have higher-velocity absorption onsets, consistent with a decreasing ionization parameter with radius in an accelerating outflow. There is evidence of strong absorption in the BEL component which indicates a high covering factor for absorption over two orders of magnitude in outflow radius.
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