This is not possible because you don't have the software that can do it.
Exim is a mail server. This is to transfer mails from point A to B. And to store mails in a local storage system (mbox, Maildir or some exotic database). Then you need a software accessing the mail storage for presenting the mails to users. These kind of software is an IMAP or POP3 server.
If you chose dovecot as IMAP server (I would) you can use a migration guide to convert your mails via IMAP to the new storage. This will not migrate the users/passwords, no calendar, no todos, no addresses and nothing else! Shared folders are very hard to migrate and probably only will work by configuring manually.
This migration path is not a step-by-step "click-click-ready" guide. You definitely need special batch files (on the command line) that do the transfer. You have to think about it, make migration plans, evaluate your options, test thoroughly, migrate carefully and then intensively train you users that everything is different than on Exchange.