We bridge the light-front (infinite momentum) and rest-frame descriptions of a heavy quarkonium, spanning them to any quarkonium momentum. For a relativistically moving system with nonrelativistic internal motion, a relation is established between the potentials describing a heavy quarkonium in the rest and moving reference frames. We explore two regimes: the small coupling and nonperturbative small binding energy approximations. In both cases a consistent picture emerges. The results, in particular, can be applied to the description of the final-state interaction of a heavy quarkonium produced in a nuclear or hot-matter environment. It can also be extended to the description of the final-state interaction of other weakly bound systems, like the deuteron.