When you use the Content Layout editor you are editing the content, specifically the post body, of an individual post or page.
What you create for that post is unique to that post (it literally is the post).
If you want to re-use the design for different posts then you should be creating a Template Layout that can be re-used across multiple posts. (It doesn't have to be used for all posts, you can manually assign it to individual posts when you edit them.) Use the post content cell in a template for the part of the design that is particular to each post, i.e. the contains the specific post content.
If you have a design you created for one post and you simply want to use it as the starting point for one or two other posts and you don't want to create a template, you can use a plugin such as Duplicate Posts to clone the original post, and then you will have a second post with the same design.
If you want to move the post design to another site you should be able to use the normal WordPress export/import tools for copying post content. (The module manager and Toolset export/import tools are for copying templates and settings, not for post content.)
Given the above options I'm pretty sure a request to add import/export functionality for individual Content Layouts wouldn't be accepted.
Am I missing something when it comes to what you aim to do?
Thx for your quick and clear answers.
My use case is in fact when I want to export the design to another page. And your answer is clear, I should do this by exporting the content. I will try to find a good way to export only one post.
Thx again.
This ticket is now closed. If you're a WPML client and need related help, please open a new support ticket.