Directional light does not cast dynamic shadows after origin rebasing using world composition.
There is an attached project that reproduces this. To see that the shadows load primarily where the level is opened you can open the Level's panel and double-click the "StreamingLevel2" to the FarFarAway level. If you hit PIE here you'll see that no shadows cast at the StreamingLevel1 but do at the StreamingLevel2 location when you shift there.
1. Open the attached UE4 Project
3. Press 2 to shift to the other level
4. Press 1 to go back.
Results: The dynamic shadows are non-existent when origin shifting
Expected: The dynamic shadows should shift when origin shifting.
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