Any progress? The task is not even started..

The problem arises in all windows with two lists: EditGroupMemebers, EditGroupsForComponentPermission, EditGroupForBranchPermission (didn't find where it's used).
Each list is created by ZK component Listbox with defined data model.Two attributes of Listbox are used to allow multiple selection in the lists: "multiple" (true) and "checkmark" (true). But according to zkoss docs (http://books.zkoss.org/wiki/ZK%20Component%20Reference/Data/Listbox#Multiple_Selection): "If you use model, the multiple attribute should set to model instead of listbox itself".

In org.jtalks.poulpe.web.controller the base class TwoSideListWithFilterVm for the description such windows is defined. It creates two model of data. Each window class (EditGroupMembersVm, ...) inherits the models. To fix the problem it's necessary to set "true" for "Multiple" attribute for each model.
The simplest way to make it - at model definition in the base class constructor (model.setMultipe("true")). In this case all window will have checkbox to multiple selection.

After fixing the problem we'll get another one: if list is empty the header checkbox is showed as checked. I couldn't fix it so far.

Okay, commit your changes and I'll take a look.
PS: please, log your work in Work Log, not in comments.

And why in general we need the selecting of header? I think it's just this header not set as 'header', because otherwise I don't know why it's allowed at all to check it.

It's a typical behaviour of ListBox component. The question is should we change it or not? HeaderCheckedExample.png contains header checked example with empty list.

Ideally, the box should be unchecked. If you know the means how to correct this, please do it. But don't spend much time on this.