re: Booking Flight Segments Separately

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For the London-DFW flight, book the American flight that leaves at 12:50pm instead of the british airways flight that leaves at 11:50am. I'm not sure if there's an interline agreement between American/Croatia where they will automatically transfer your bags. You may have to pick them up in London and then go back through security

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Regardless, you will need to change terminals, and at LHR that means you will need to clear immigration and security.