The Jovian-sized object WD~1856~b transits a white dwarf (WD) in a compact $1.4$-day orbit. Unlikely to have endured stellar evolution in its current orbit, WD~1856~b is thought to have migrated from much wider separations. Because the WD is old, and a member of a well-characterized hierarchical multiple, the well-known Kozai mechanism provides an effective migration channel for WD~1856~b. Moreover, the lack of tides in the star allows us to directly connect the current semi-major axis to the pre-migration one, from which we can infer the initial conditions of the system. By further demanding that successful migrators survive all previous phases of stellar evolution, we are able to constrain the mass of WD~1856~b to be $simeq0.7-3M_{rm J}$ and its main sequence semi-major axis to be $simeq 2-2.5$ au. These properties imply that WD~1856~b was born a typical gas giant. We further estimate the occurrence rate of Kozai-migrated planets around WDs to be ${cal O}(10^{-3}{-}10^{-4})$, suggesting that WD~1856~b is the only one in the {it TESS} sample, but implying ${cal O}(10^2)$ future detections by LSST. In a sense, WD~1856~b was an ordinary Jovian planet that underwent an extraordinary dynamical history.
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