Pocketbook can hilight text in pdfs, while reading on it, but it seems that this hilighted text is not saved on pdfs which are taken back to zotero through zotfile and through Dropbox synced file.

No, I don't see annotations. Meanwhile, I had the following recomendations from PB support:
"1. You can export notes in .html format and open them on your PC.In this case you need to do the following : go to the application Notes select the option "Export notes" check the corresponding checkbox for each note that you need to export; tap on "Export" choose the folder for saving (you have the internal memory/Notes by default) please confirm notes export by clicking on "Export".Then connect your device to the Pc or a laptop and export the notes from the folder.
2. Dropbox supports books synchronization only. It means, you can add books from Dropbox, but it does not synchronize the notes, bookmarks and reading position...."
The first point is quite troublesome, allowing no integration with zotero standalone app. The second leaves no other choice than synchronizing notes through one more account on their cloud. End of story, no big help from PB. Hope you come up with a better solution. Thanks.

@steliosdimitriadis your second point is not correct (anymore). If you export your notes to the Dropbox folder and sync the exported html file will be synched.