Hi Kris_Gatchev , not sure what do you mean by "2 way"? This would be an "one way" type of migration as explained below. And I don't know if we have an official documentation that specifically describes this but I am assuring the information below is correct.
During an IMAP migration we have a synchronization process between source and target, the changes are unidirectional, coming from on-premises IMAP server --> to Exchange Online. If during an IMAP migration, the end-users or admins delete content from source IMAP mailbox / server , the deletions will be synced to O365 as long as the synchronization process runs (you can see it with Get-SyncRequest -Mailbox <user>). The Synchronization is active as long as the migration is ongoing (migration batch is not deleted or the Sync Request is not being removed). All the changes reported in source are synced to EXO and you can see it with Get-SyncRequest -Mailbox <user> | Get-SyncRequestStatistics -IncludeReport or from GUI.
If data has been inadvertently deleted from the source, the deletions are processed during initial or incremental sync as expected and MRS Sync Request is hard-deleting it from target as well. Engineering team will in the future address this, not to hard delete anymore the data deleted on source so that customers can recover the data from Exchange Online Mailbox, even if this is gone forever from source. For the time being, customers should try to recover it from the source side, where the original content has been initially deleted from.
Exchange Online MRS Sync Request only replicates the changes (deletions / additions / folder hierarchy changes etc) and it is not responsible for the (un)intended deletions which happened on source.