For those who are facing my problem, in order to translate your module, you need to do the following:
- Find the folder {root-of-your-joomla}/language/en-GB
- There search for the two translation files of the JA K2 Filter extension, which are:
- en-EN.mod_jak2filter.ini
- en-EN.com_jak2filter.ini
- Copy those files in a folder inside {root-of-your-joomla}/language/ which is corresponding to the language you want to translate to. For example, for French it would be fr-FR, for German it would be ge-GE, for Russian ru-RU etc.
- Rename the files, changing the en-EN with a prefix for your language (like in point 3)
- Open the files and change the text between ""