@Anhalter, is it still open? I know there used to be one but I don't recall seeing it last time I went through and what I found online it says that it's probably closed. But I still tend to search in English, my German is pretty average...
They do list:
Deutsche Post Filiale 635
P & B Press & Books
Open M-Sat 9.00 - 18.00, closed Sundays
They're listed as a DHL Agent
Up to 10 kg , 120 X 60 X 60 is quoted as €10.49, up to 31,5 kg max €19.99 - same dimensions.
However it is possible that if you have protruding parts for example wheels, handles; & no external packaging of cardboard or paper that they will treat it as a bulky item which costs significantly (€30.00) more. Also the suitcases are not insured for damage to the case itself.
You could of course custom make a box for it, pre-address it and then pack it in the carry-on bag along with some tape and package it once you're in Frankfurt Airport prior to posting.
Suitcase should be closed with zip ties not padlocked. No idea why?
Or, simply use a foldable bag as your carry on and send two packets as shown by Anhalter above
https://g.co/kgs/9x3T2t
@maysie123 , suggest you get your brother to double check this!