Stuck on reinstallation of OS X 10.11.6 El Capitan
The processing steps sketched below fixed the issue.

Hardware-Software-Environment

MacBook Pro Early 2015 running OS X 10.11.6 El Capitan.
The internal HD is actually a 250 GB SSD comprising partitions EFI, Macintosh HD and Recovery HD. There is no encryption enabled on any of these partitions.
 At the time we started the reinstallation attempt described here, the Macintosh HD partition is unusable as startup volume due to a previously stuck installation attempt, see question above.  

Processing Steps  


We boot the machine from a startup volume residing on an external HD connected via USB 3.0 Bus. Then we log in to a session in Normal Mode under OS X 10.11.6 .  
We download a new El Capitan installation package from 
http://updates-http.cdn-apple.com/2019/cert/061-41424-20191024-218af9ec-cf50-4516-9011-228c78eda3d2/InstallMacOSX.dmg  
We unpack the package to install the macOS installer.  
Now we just run the installer; Internet connection off. The machine rebooted and, after approximately 30 minutes, reappeared with a login screen.  
We could verify that OS X 10.11.6 BuildVersion 15G31 had been properly reinstalled to the Macintosh HD partition with no user data or previously installed third party software lost.  


Reference
How to upgrade to OS X El Capitan

Acknowledgement
Thanks a lot to @Udhy for the decisive hint to fix the issue.