Custom Sidebar Pro: Does it work together with WPML?

Wordpress 4.4.3, Custom Sidebar Pro, Holder Theme 1.1.8 (Child Theme)
I have a website in four languages with WPML. So in the Holder theme I have four different menus (for each language one main menu) which show up in the sidebar whenever a normal post of the respective language is shown - all is well.

Now I have a new custom post type "events" (from plugin Events Manager).
I want to show a different sidebar for posts of type "events".
The "Event Sidebar" should have a new "Event Menu" (which just has the links to the main event pages). I can make this Event Menu in all four languages.
In addition to the Event Menu, the Event Sidebar has a link to the Event Shopping Cart.

How do I get the Event Sidebar shown on the custom post type "events" in the four languages?

I tried Custom Sidebar Pro to define a new sidebar "Event Sidebar" with the english "Event Menu" (and the shopping cart link) and showing this sidebar only at the event post types. Works perfectly in english!
But when I switch the language to e.g. German, then the Main Menu in German is shown (and not the Event Menu in German).

When I look at the Widgets page with language German selected, then the "Event Sidebar" has no entry for the event menu. When I change it there to the German "Event Menu", then it shows up perfectly in German, but in English not - the widget for the Event Sidebar then has no entry for the event menu again.

From that I conclude that the Custom Sidebar Widget does not come in translated versions.

What I tried also: Make two different custom sidebars - one in english, one in German. But the sidebars both want to be shown on the events custom post type (there is not option in Custom Sidebar Pro for choosing a language). And so this does not work either.

Any hint or help in this situation?
Thank you!