How to send exim mail via gmail to specific users?

Question

Exim

Hello, smtp exim4 + pop3 dovecot is running on the debian squeeze
server Let's call this server mx.site.ru
The server serves mail for users and domains.
[email protected]
[email protected]
[email protected]
Through the mail client, users receive and send mail on this server.
Task:
Make it so that when sending mail from the [email protected] mailbox to the external smtp * @yandex .ru, it is not sent directly from the server and the [email protected] mailbox to * @yandex .ru, but through the gmail account.
So that the recipient of the letter sees the gmail account as the sender.
For example:
[email protected] is configured to forward incoming emails to [email protected]
it is necessary to send a letter to vasya @yandex .ru
the letter must come from the mail [email protected] (the mailbox is registered)
through the mail client [email protected] sends mail to the mailbox [email protected] and then it goes from the server through fedya
@ gmail.com