Both .zi and .pzip files are sometimes just renamed ZIP archives. So you actually do not need to convert one to another, but rather rename the extension to ZIP should you need it. But otherwise, this zi to pzip conversion does not make much sense.
Convert Renamed ZIP file to Zip compressed archive file.
We have found one software suitable in our database for this conversion.
Apple macOS / Mac OS X software - convert zi to pzip on OS X
Mac version of the popular WinZip compression utility.
Convert from zi file format
The table with program actions contains information about what each program is capable of doing with their files. This may be a good pointer for further searches for certain file conversions and help you find the converter you are looking for if our search result is insufficient for you. However, it is far from perfect and may sometimes show results which are not really usable because of the nature of the software handles the files. So a conversion that appears as possible, just because of matched actions, may in fact not be possible.