I have been connecting from elsewhere in Europe, through FRA or LHR on my way back to the US for years now.
Regardless of the combination of carriers used, I will not pay the departure tax from FRA or LHR as long as I am a through passenger (24 hours of layover max) and can prove it.
For example FCO to LHR on BA ,then LHR to DFW on AA= departure tax at FCO,no departure tax at LHR.
The only proof at the counter has been the boarding pass with my name on it.I always keep my zed tickets also,just in case.
At AA we fly ticketless.Twice I had the tax incorrectly charged at LHR and FRA,and after supplying zed ticket and boarding card to our travel department,I received a refund.
Happy travels.
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