Thank you for the answer.
Checking mail is what I do with the test registration.
At test registration CB gives a message
"Sign Up Complete!
An email with further instructions on how to complete your sign up has been sent to the email address you provided...." But the registration letter doesn't come and you can't see it in Logs.
Asked the hoster a question, he answered:
>I:Is there a blocking of outgoing spam on the mail server ? I mean, can the registration email be considered as spam and blocked?
>H:No. No.
>I:In DirectAdmin under Mail Reports / Logs, should I see the emails sent when a new user registers?
>H:Yes, if your site code works properly. But it does not work properly.
Yes, it is also important, if now the site is deployed to the localhost from the backcopy site, the mail works as usual. User registration in CB also works. SMTP settings remain the same.