Is there any way to add article to many categories?

Only via an extension called K2 Additional Categories.
extensions.joomla.org/extensions/extension-specific/k2-extensions/22204

OK.

I installed it and it works for existing articles.

But when I want to create a new one I get an error :

" You have an error in your SQL syntax; check the manual that corresponds to your MySQL server version for the right syntax to use near ')}' at line 1 SQL=SELECT `catid` FROM fabu_k2_additional_categories WHERE `itemID` = {intval()}".

Any idea?

Since this is a 3rd party extension, the developer will provide a solution.