I had recieve the error
#< #5.1.3 SMTP; 553 sorry, your domain does not exists.> #SMTP#
What does this means?
It is a message from server with sendmail, send to domain3 (which uses ms exchange).
Full error mail from exchange (sorry, not exact message, but translated from ru to en)
Diagnostic info for administrators:
Forming server: domain1_with_sendmail
user@domain3
#< #5.1.3 SMTP; 553 sorry, your domain does not exists.> #SMTP#
Does Exchange change text description from remote smtp error?
There is "MX" record for domain3 and no "A" records for domain3, only one for "www.domain3"
Update" all domains are public and have fully-qualified names, all dns's are accessible."
Update2: domain1 has only "A" record, but not the MX one. Can it be a problem?
The error message says that your domain does not exist. This means your HELO or reverse DNS has issues (or) there are DNS problems with the recipient Email server. If it is an issue at your end, try this Email Server Test and it will tell you what is wrong.
Where is your MX record stored? Presumably on a local DNS server, as domain3 isn't a public domain. In which case, check where your server is doing it's DNS lookups. If it is going straight to a public DNS server, then you will see this message.
Assuming that domain3 is not just an example.