Both iMessage and SMS messages addressed using either a phone number or Apple ID associated with the same Apple account should appear on any Apple device logged onto that account. … Are you certain about SMS messages appearing on a desktop (no cellular service) Mac? I have yet to see them on any iMac or non-cellular iPad.
On a Mac since 1984.
Currently: 24" M1 iMac, M2 Pro Mac mini with 27" BenQ monitor, M2 Macbook Air, MacOS 14.x; iPhones, iPods (yes, still) and iPads.
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