What specific version of SmarterMail 16.x are you using?

Pascale, can I have you open the developer tools in the web browser?  This is accomplishing by inspecting on the web page itself or pressing F12 in most Windows browsers.  Then make sure the Network tab is selected.  Try to perform the contact export.  If any of the API calls are failing, it should be annotated in red with a 400 response code.  Click on the error, if present, and take a screenshot of the error--both the headers and the preview response.  This will help in tracking down the error.  Let me know if you have any questions.

here are the screenshots:

Headers

 

Preview:

 

Response:

Thank you for the screenshots.  I'm assuming that you are in the contacts page and select the ... menu then Export All CSV?   Do Domains B and C have normal users that are not Aliases and Mailing Lists?

To export contacts: i go to the contact tab, i select all contacts and i select export all CSV. It works for the domain A, but not for the others.

 

All Aliases and mailing Lists have been hide.