Move dovecot between servers

[Gandalf Corvotempesta]

Hi to all
I have a very old dovecot server (1.2.15) with about 195GB used and
1081 email accounts.
I have to move this server to another one with contextual dovecot upgrade.

Anyone did this before? Any advice? Obviously, existing emails *must
not* be downloaded twice by existing clients (outlook, thunderbird,
...)

I have no access to customer's clients, only to my server.