OfflineIMAP is described as 'OfflineImap synchronizes email between an IMAP server and a MailDir or between two IMAP servers. It offers very powerful and flexible configuration options, that allow things such as the filtering of folders, transposing of names via static configuration or python scripting' and is an app in the Office & Productivity category. There are six alternatives to OfflineIMAP for Windows, Linux, Mac, iPhone and BSD. The best alternative is MailStore. It's not free, so if you're looking for a free alternative, you could try imapsync or isync (mbsync). Other great apps like OfflineIMAP are mnIMAPSync (Free), IMAP Upload (Free, Open Source) and Softaken IMAP to IMAP Migration (Paid).
mbsync is a command line application which synchronizes mailboxes. New messages, message deletions and flag changes can be propagated both ways; the operation set can be selected in a fine-grained manner.
Softaken IMAP to IMAP Migration allows transfer of emails from one IMAP Server to another. All IMAP Servers are compatible with this application. Users can easily migrate complete mailbox folders between IMAP Server accounts with attachments.