Originally Posted by
halls120
This. re-book with LH. They will be in a better position to help you. We have experienced occasional problems with US citizens who have SOFA cards returning to Germany flying on US flag carriers.
If OP rebooks to the LH flight, presumably there would be a UA domestic connecting flight to start. Thus, UA agents, at check in and the gate, will determine eligibility to fly to Germany.
Has OP looked at what TIMATIC says about the situation? That's the source airline employees use to determine whether to allow a customer to board.