dovecot - Jun 2018 - Dovecot as transparent proxy for Exchange<->Dovecot<->Yahoo.com/Yandex.com with mail synchronization between servers !

We have Exchange as internal mail server, also we have gate where we plant
to install Dovecot, also we have external mail at servers such as yahoo.com
ort yandex.com.
There are some mailboxes at Exchange, for example:
user1 at internal.ltd to user10 at internal.ltd.
There are some mailboxes at Ynadex.com, for example:
personel1 at external.com to personel10 at external.com.
1. For messages flow:
We need that Dovecot would act as at least transparent IMAP proxy for
Exchange/Yandex and vise versa.
For incoming messages - some messages comes to personel5 at external.com
located at Yandex.com, then Dovecot gets it from Yandex using IMAP IDLE,
tnen stores it locally (where Dovecot is installed) to MySQL (using DBMail)
or at least maildir format and after that sends it forward (using IMAP
PUSH) to appropriate account user5 at internal.ltd or triggers (signals)
Fetchmail to sends forward it to specified Exchange acoount.
And so on - for each external/interla pairs of accounts
(Yandex.com/Exchange) .
For outgoing messages - Exchange send out it using Exim4, Exim4 stores it
locally (where Dovecot is installed) to MySQL (using DBMail) and then Exim4
sends it out to Yandex.com and in the same time Dovecot uploads this
message to Yandex.com to "Sent" folder. And this messages is sent
through
Yandex.com.
2. For messages storage:
When messages are deleted at Exchange, it are deleted from Dovecot (MySQL
storage) and deleted from Yandex.com as well.
Or when messages are deleted from Yandex.com, it are deleted from Dovecot
(MySQL storage) and deleted from Exchange as well.

Is it possible to set up Dovecot and may be some other soft (Fetchmail,
imapsyncd and so on) to get point 1 working or point 1 and point 2 working ?
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