I stopped reading your post at “his system is S1…”. The Move only runs on S1 if downgraded. By default it is set for S2. Move2 is S2 only. 
 

Edited to correct: Move needs to be downgraded to S1 in order to run there. S1/S2 compatibility here: https://support.sonos.com/en-us/article/sonos-s2-compatibility?language=en_US

Mine are not Move2 so the downgrade was an option but I was hesitant to downgrade because I don’t understand exactly what would be downgraded and what the implications would be when I got back home where I have the app on an iPad and my wife’s iPhone. As it was, I had no trouble reconnecting at home.

I don’t think it’s irreversible, but if you didn’t do it, and didn’t change wifi credentials, I’d certainly expect it to reconnect to your S2 system without issue. 

Do you know exactly what is being ‘downgraded’?  Is it just the controller app?  Or is some capability of the speakers themselves being suppressed?

As I understand it, the “controller app” is the S1/S2 software on your phone. That’s fundamentally all it is: a controller. You use the controller to tell the speaker what to do - stream music from a particular source, increase volume, etc. The software (firmware?) l on the speaker (together with the processor etc) does the work. That’s what gets “changed” in a S1/S2 change, or in a revision upgrade to the speakers. 

That’s helpful background.  Thanks.

Still some unanswered questions in my original post of others want to chime in.  But this is helpful.

Don’t fuss with downgrading your MOVE’s for this demo. A quick and straightforward method would be to power down your friend’s SONOS units, then attempt to use your SONOS controller to operate your MOVE’s on his network. You’ll be prompted to add his WiFi to your units. Once this is complete you can power up his system and control each system with its usual controller. Avoid adding a unit to either system or setting up a new system. And, don’t Factory Reset anything.

I have an S1 system at work. It took less time for me to enable an S2 unit from home to run at work than to type this reply. When I returned the unit home it informed its mates about the ‘other’ network. Now I can simply take a home unit to the office, apply power, and start playing my usual online music on my unit.

I’ve never tried this but you should be able to connect your Synology to his network without any fuss and play your music on your units. Attempting to allow his system to use your Synology will involve some fuss. For me it would not be worth the trouble for this quickie demo.

After the demo you can just pack your units and take them home. Back at home simply power up. The units will figure things out on their own.

That sounds very promising!  Powering down his units was something we hadn’t tried.

...and factory resets are always my last (i.e. never) resort unless everything is broken.  I’ll be leaving my Synology router at home. Life is complicated enough.

Sorry, I misread and was thinking that your Synology was a hard drive. Definitely don’t take your router.

No worries, buzz.  Your strategy makes sense to me (unencumbered by deep knowledge of the Sonos architecture). It’ll be a few days before I can try it again, but I’ll get back to this thread with definitive responses, ‘likes’, ‘best answers’ and more when I try again next week.

-=Rich=-

Coming back with follow up as promised.  Today I was able to test your approach, buzz, and it worked as advertised. (But it probably took a minute or two longer than your apparently prodigious typing skills must be .)   Seriously, though, simply turning off his Sonos equipment set me free to trust his network and then use my S2 controller app.  It worked like a charm and he loved the speakers.

...side question… I was going to mark your answer as the best answer, buzz, but that had already happened.  Can anyone just pipe in and mark my question as answered on this forum?  Seems a little odd since I hadn’t proved that it worked. (I kinda thought it would, but wanted to be sure before others relied on it.)

No, only yourself (as the thread Author) or a Sonos Moderator on the forum can mark a reply as the best answer.

Unanswered questions are routinely reviewed by Sonos mods and marked with a best answer from the available replies (as long as it does answer the question correctly), otherwise the mod would reply and mark their reply as the best answer.

And honestly, @buzz is always right ;)