Thank Again Dmitry! 
I re-build the image after copying the cache.key to the install folder (where cinstall_silent resides). During the docker image build, it correctly print the Organization name as licensed.

Also, inside the running container, when I issued the "csession <instance-name>", nothing happened. The Alert log has the following entry.

04/23/19-12:51:47:259 (876) 3 Process 876 (JobType=Interactive job (programmer mode),Directory='/opt/healthshare/mgr/') caught signal 11. If core dumps are enabled, a core file will be created by process 877 in the location specified by the system configuration.

Anyway, I will try find if I can get the latest version of HS.
 

Thank you so much Dmitry for your quick response!

 Following is the logs I captured when building the docker image. It seems, it is complaining about "License missing or unreadable". 

....
Starting up HealthShare...
Once this completes, users may access HealthShare
Using 'cache.cpf' configuration file

This copy of Cache has been licensed for use exclusively by:
License missing or unreadable.
...
...
Installation completed successfully
 ---> f2c7971c5194
Removing intermediate container 38f300e31474
Step 13/21 : COPY HS-Install/cache.key $ISC_PACKAGE_INSTALLDIR/mgr/
 ---> 1aae89597d95
Removing intermediate container bb195b168e18
...
...

 Do I need to copy the cache.key file before the following command? 
  RUN ./cinstall_silent ....