WPML and PublishPress Permissions Pro
PublishPress Permissions Pro does have support for the WPML plugin.
By default, PublishPress Permissions Pro will automatically mirror your post / category permissions to the translated content.
So, if block users in the “Author” from editing a post, they will also be blocked from editing any translations of that post.
Normally you will set these permissions under each post, using these boxes.
By default, these boxes will not be enabled for translations because the translations are simply using the same permissions as the original post.
This feature can be configured by going to Permissions > Editing > WPML Integration:
If you uncheck these boxes, each translation will have separate permissions boxes.