Thank you Jacob for your reply.
I can login to web mail with my account firstname.lastname@example.org with the same password of mail settings in opencart. The form on the web site, as well as the cart for the online orders, are linked to email@example.com. Would you please try to fill out the form on the web page to check if the form sends correctly the email? You can change the language from It into En from the flag above the main logo.
We checked today and we did not get the emails on firstname.lastname@example.org from the contact form.
Also, the emails on the gmail.com account were not in the spam and were neither received. I want to let you know that the domain has been suspended for more than 2 weeks cause a registant change. The site started to work correctly again last Thursday.
Except for this situation we did not edit anything in the last weeks. Today we tried to restore the site using softaculos, sure to solve the problem, but it did not work. The account email@example.com works correctly but orders coming from the cart and emails from the contact form are not working.
Thank you again for your help. BR