Problem with sending and receiving messages

Hello,
When I enter in the “Your E-mail” field:
[email protected] or other email address created on my server, sending messages works correctly. If I add an email address without my-domain, then the sending does not work.

PHP – displays a message about sending a message, but I do not receive messages and I get a message about not delivering messages. A fragment of the message returned by the server: “Sender address rejected: Your server can not send mail from [other-domain] (in reply to RCPT TO command)”.

SMTP – An error has occured when trying to send email:
>> SMTP error: The following recipients failed: [custom-email-address] :: Sender address rejected: username [my-smtp-email].

It looks like the plugin wanted to send a message from the address provided in the field: Your E-mail.

What could be the reason for these problems?

Can the plugin have such functionality?
(wordpress email) From: [email protected]
(your e-mail) Reply to: [email protected]
(friends e-mail) To: [email protected]

Regards