GoDaddy to Hostinger Email Migration

I have five active business email addresses hosted on GoDaddy that must be moved to Hostinger without any loss of messages or noticeable downtime. Each mailbox needs its full history—every folder, attachment, and archived item—copied over so users can pick up right where they left off... (Budget: $10 - $30 USD, Jobs: Asterisk PBX, DNS, Email Handling, GoDaddy, IMAP, Linux, System Administration, Technical Support, VoIP, Web Hosting)