Hi rg305,
thank you very much for your reply.
Yes this sounds also as a solution, but I read it too late. Sorry I found a other way.
My misunderstanding was that I expect, that all necessary information are stored in the p12 file or in the operation system. It is not 
I also need to provide the intermediate and both root certs during the call of sapgenpse like this
./sapgenpse/sapgenpse import_p12 -r root-isrg-x1.pem -r inter-letsencrypt-crt-R3.pem -r root-dst-ca-X3.pem -p SAPSSLS.pse -x "" sap_wildcard_cert.p12
What I still not understand is that in the old call of sapgenpse also three certificates was provided. The "DST Root CA X3" should be one of them, because it was also used in the old p12 file. But in fact it was not one of the provided certificates. Hmm. Strange.
I hope it was not so much time wast to write this hole article here and it helps somebody in the future.
Thanks again at rg305 for reading and understanding my article!
Enjoy your day 