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I believe that Groups.io does forward them to all mods/owners, including the sender when that is one of the mods/owners. Subject to the individual mod/owner's Owner Email Subscription setting of course.

The situation you face is (I think) slightly different than Gary's. Where Gmail accepts but hides messages that you sent upon their return (as from an email list or forwarding) Outlook has been reported to reject such messages outright. The logic being that it must be a forgery if it claims to be From your address but was delivered to them by another service (Groups.io). For this case a different work-around would be required - Groups.io would need to replace the From field with one that isn't your email address.

If you receive your own group postings back at Outlook that would imply that Groups.io has implemented some work-around, or convinced Outlook to "play nice" with group postings, to overcome the problem that was reported earlier (Outlook users seeing their own messages in their Bounce history).

Shal