Connecting to a delegate accounts via MAPI is a supported feature in Aid4Mail and is well documented in the Aid4Mail help file.
Now connecting to a shared/delegate account via O365 via IMAP is not officially supported by Aid4Mail but we and other clients of ours have had success using the below syntax.
In Aid4Mail you can try using the following format for your username (after selecting "IMAP" as your "Mail Source" and selecting "Office 365" as the "Imap Settings"): Username@DomainName\SharedMailboxAlias
It can also be that you need to add the domain for the SharedMailboxAlias like this: Username@DomainName/SharedMailboxAlias@DomainName
The password would be for the main user/admin (not the shared/delegate account). Here is how it looks:
If you have any questions or issues, please contact us by raising a ticket.