Possible problem when a leglit ZS user can create test, but not to be assigned to execute the test

That sounds odd.  I don't know why that's happening, but I would do some testing to try and narrow things down to find the source of the issue, e.g. moving them into another group, etc., but first of all check that they have been added into the Project as a User (Project Settings > People).

There's always the smartbear support team too.  you can contact them here: Support Portal