How signatures are added to emails sent as / on behalf of other users
Sometimes a user or a group of users have permission to send messages as other users or on their behalf. These users are referred to as delegates. See the examples below to learn how the software works for users with delegate permissions.
Example 1: User A has the Send As permission to the User B's mailbox. When User A sends an email and enters User B's email address in the From field, the message will be considered as sent by User B. Therefore, the rules covering User B will be executed (the email will get User B's signature) and the SIU service will update the message in the Sent Items folder of User B.
Example 2: User A has the Send On Behalf Of right on User B's mailbox. When User A sends an email and types the email address of User B in the From field, the message will be considered as coming from User A, and the rules covering User A will be executed (the email will get User A's signature). The SIU service will update the Sent Items folder of User A.
If you want to know more, see our Knowledge Base article for examples with screenshots.
In order for the SIU service to work as described above, you need to enable message copying in your Exchange Online, as described in this Microsoft blog article.