In Office 365, you have the Inbox folder containing all the received emails. You want to move all emails received in 2018 and earlier to a different folder.
You would like to know whether these emails would be saved anew in the next incremental backup.
When emails are moved from one folder to another, Office365 considers them as new items and they will be backed up in the incremental backup.
When the entire folder is moved from one parent folder to another (ex. inbox/folder1 to inbox/folder2/folder3), structure of content in the archive will change while the emails in inbox/folder1 will not be backed up anew in the incremental backup.