“docker cp” all files from a folder to existing container folder

Here is the explanation from the doc on how to use the cp command in docker, which will fix your issue with /. at the end of SRC_PATH:

• SRC_PATH does not end with /. (that is: slash followed by dot)
  • the source directory is copied into this directory
• SRC_PATH does end with /. (that is: slash followed by dot)
  • the content of the source directory is copied into this directory