Hi Ulf,
That would qualify as a feature request, and should go into that forum.
Since sign-up sheets are NOT a custom post type (but, rather, stored in their own custom tables), there is no way in the current database structure to set the author of the sheet.
So, this new idea/feature would require quite a bit of code change, as well as a database table upgrade. Each sheet would need to have an “author” type of field to save the user id of the person creating the sheet. Then, we have to go back through all the admin side code and add additional checks to see if the author matches the current user before they are allowed to edit that sheet.
But, then what happens if there are several chair people for an event/task? Then we need to be able to check against multiple author ids. In that case, it would probably make more sense to create a small relational table that saves sheet id and author/id so there could be any number of authors.
Not possible in the current release of the plugin, but feel free to add it to the feature requests.