Message replies go to wrong device

Thank you for providing a very clear explanation of what you're doing and what you're trying to accomplish.

Peter Oram1 wrote:

I frequently use Messages to send a message from my iPhone to my partner's iMac.

Your screen shot clearly shows that when you send a message from your iPhone, the "Start New Conversations From" indicates it will show up as coming from your telephone number. So when your partner replies, it will be sent to your telephone number.

However, the screen shot of your Mac clearly shows that you have not checked your telephone number on your Mac under "You can be reached for messages at."

So naturally your partner's responses will not show up on your Mac.

I'm terribly sorry ... I clearly didn't thoroughly understand your question. You wrote it so clearly - I apologize again.

I suggest your partner check your address as (s)he replies to your message. Perhaps (s)he can click on your name if it appears at the top, and if a circled "i" appears, click there and be certain only your phone number shows up as an acceptable address to respond to.

What caught my attention about your many helpful screen shots above is the presence or absence of your country code +61 (Australia) from the telephone numbers in various circumstances.

Might you have an explanation, such as doing international travels, international dialing, or some such thing? I'm wondering if that might be related to overriding your specification of the telephone number and changing to the manager address, thinking perhaps you're being aided by not having to do something internationally.