I am able to reproduce it.
This seems to be a bug that is araised with Joomla 3.4 and higher.
Modification in the Article Sharing is therefore required to be compatible with J3.4 and higher. This will take a little time.

A partial fix is available in the Article Sharing version 1.3.08 that fix the JavaScript error under Joomla 3.4 and higher.

Temporary workarround to create a new menu item using the "Multisites single Article Layout".
Ensure that you have at least one article in your current site.
When creating the menu item "Multisites single Article Layout", you can select the "Site ID" but the "Select Article" does not show any articles.
Click on the search icon that displays the article from the CURRENT site (Not the selected site). That is BAD but give you the possiblity to provide an ID that is mandatory to save the menu item.

Select any article to have an article ID and save your menu.

Re-open the menu item and now you will be able to see the list of the article for the selected site ID.
Do not use the Search filter as it display the current site article ids.
If you enter something in the filter, you have to close the modal (popup) window and re-open it to have the value filtered on the appropriate Site ID.