I thought maybe you could write your string to a file, then add both files to a .zip file. However, it doesn't appear that you can compress more than one file in the created .zip file. Try running the examples in the docs--they create a separate .zip file for each input file.

It's not clear to me what your objective is. Do you want one file containing all the data to be zipped? Or do you want the zip file to contain two files? If you want one file with all the data, first append your string to your file, then zip it.

The documentation for that module is horrible. I can't believe they let a module into the core without having some minimum standard of documentation.