Thanks again for problem solving and the suggestions. I apologize that this is incredible long but I hope the information helps you and others who might find this a challenge. Here’s some additional information.
First: I set up a new account on my MBP so all preferences would be at default. I logged in to Apple ID and configured Messages in iCloud. It took a while but all of my text messages downloaded EXCEPT the one I’m trying to recover. But it clearly sync’d the new account with iCloud. Question: Could I test the uncheck “Enable Messages in iCloud” option in this new account or would it have the same effect as my administrator account, both using the same AppleID for Messages?
Second, my partner and I share the same Apple ID. We configured his phone so Messages are NOT on in iCloud so he can delete them at will on his device but not mine. He gets all of my messages through our Apple ID AND my iPhone. I looked at his iPhone recently deleted conversations and there was the conversation in his deleted list that I want to recover on my MBP. I was able to restored it on his phone, all 120 messages in the conversation. Messages is ON in his Messages settings. So it would appear the full conversation is in iCloud under our Apple ID and can be retrieved on iOS, evidently not OS Big Sur.
Now to the interaction you suggested between Messages on my MBP and my iPhone (where the desire message still is populated). I can’t fully test this on my partner’s MBP because as I stated above he does not use Messages in iCloud. All devices share the same Apple ID. Message sent from my MBP: message populated on all devices. Same conversation deleted from my iPhone: Deleted conversation on my iPhone and MBP but none of my partner’s devices (remember, he does not have Message in iCloud). Message sent from my iPhone: message populated on all devices. Same conversation deleted on my iPhone: same, result.
Now my MBP: Conversation deleted. Did NOT delete from my iPhone. This is what happened with the conversation if deleted by mistake. Now my iPhone: Conversation deleted. Deleted from iPhone and MBP. So the sync mechanism initiated by my MBP to deleted a conversation isn’t syncing to my iPhone.
On my partner’s MBP, I created a new account, logged in to AppleID and the set Messages to Enable Message in iCloud. Messages took a while to download but unfortunatley, the desired message is NOT there. Right now it is only on my iPhone. Why?
My situation may be rare (like being a dinosaur). When we started with Mac’s, they advised using the same Apple ID for a number of reasons, but perhaps that is a problem now with Messages and other apps.
OK, this is a Apple developer puzzle? Botton line, sometimes the chase is more exciting than the catch. I enjoy a challenge but this is off the charts. The deleted conversation is still on my iPhone so I can refer back to the 120 messages in the conversation. If you want to call it quits, I totally understand. Thanks for helping me try to figure this out. I hope others find it interesting and challenging. Regards, Rod