Iredmail moving to miab

Good afternoon, please tell me if I can transfer the backup copy of my mailboxes from iredmail to miab
is there any compatibility?

The easiest way is probably to use a tool like imapsync which you can use online or install locally. That way you don’t have to worry about compatibility of mailboxes.
That said, from a quick glance at iredmail I think it is using dovecot, just like Mail-in-a-Box. This means it is probably possible to figure out a way to transfer the mailboxes the hard way.