You´re right - ashes on me - ...

But he´s still on the safe side because the airline (LH in this case) has issued the ticket that way.
Online-connections are always better than interline-connections anyway. So, LH to LH is certainly the safest connex possible via FRA. Especially since it´s LH´s main hub!
The worst thing that may happen is due to late arrival of the inbound flight he won´t make it and get rebooked to the next flight one hour later ...
(second worst case: his luggage won´t make it on the same flight to TXL and arrives 1hr later...)

So, no problems i would worry for too seriously - just very little "discomfort" in case he or his luggage don´t make the connex.

But if flights are on time - nothing to worry at all ! Since all is done within the same terminal !