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People would just assume you lost a limb, which is not usually visible with your clothes on.

conservation of momentum is only a true, when translational invariance holds. In addition, there may be a countless number of mechanisms by which teleportation changes a persons momentum. E.g. maybe the way this kind of teleportation works is Star Tek-like and your atoms get disassembled and reassembled, meaning they don’t need to have the same overall momentum, when whatever is doing the dissassembly stops atoms for dissassembly.