Currently messages forwarded using the Simple Mail Transfer Protocol (SMTP) or mailbox forwarding are rewritten so that they come from the forwarding mailbox.
However, Microsoft is currently working on a new email upgrade that will see messages that are autoforwarded (or redirected) in Office 365 rewritten using the Sender Rewriting Scheme (SRS).
Sender Rewriting Scheme
This new SRS feature rewrites the P1 From address (also known as the Envelope From address) for all applicable messages that are sent externally from Office 365. As a result of this change, deliverability of messages that pass SPF checks when they arrive from the original sender but then fail SPF at the final external destination after they are forwarded has been improved.
Still though, due to changes in behavior, disruptions may occur. For instance, forwarded messages will no longer be rewritten when sent to a customer’s on-premises servers.
Microsoft will begin using SRS to rewrite all messages forwarded using SMTP or mailbox forwarding beginning in October, so if you’re forwarded emails don’t arrive at their final destination at that time, this could be the reason why.