CKEditor Anchor Link breaks some Core ckeditor shortcut menus

I've noticed that using the link button provided by the CKEditor Anchor Link module instead of the one provided by the core ckeditor module breaks the link editing shortcut menus.
Here are the steps to reproduce the issue:

Without the module:

1. Open an edit form to create a content. In the ckeditor edit window create a link and save it.
2. Staying in the same window, highlight and right click on the newly created link and notice the "Edit Link" and "Unlink" shortcut menus.

With the module installed:

1. Install and enable CKEditor Anchor Link Module
2. In configurations replace the default "link" and "unlik" buttons with the new ones provided.
3. Open an edit form to create a content. In the ckeditor edit window create a link and save it.
4. Staying in the same window, highlight and right click on the newly created link and notice that "Edit Link" and "Unlink" menus have disappeared.

It'd be nice if this fix was included while refactoring this feature.