Sonos Move 2 compatibility with video projector

If you want to use Bluetooth, as mentioned in your post, you would need to attach a Bluetooth TX to the Optical-out port and pair that with your Move 2 speaker - it maybe okay, but it’s a case of trying it and see if it works well for you.

The good news is you can go onto feed the BT stereo/mono audio-in into any Sonos product (in same Sonos Household) whilst on the same WiFi network. 

Note: the Move 2 also has an analog line-in option aswell (using a Sonos audio dongle), but I would not personally recommend using that with the projectors 3.5mm audio-out, as that would result in an audio buffer delay of at least ~75ms and may (likely) cause you lip-sync issues with any video on screen. 

So Bluetooth is ‘possibly’ one way to go, but it might present some reliability issues, or occasional drifting out of sync, but worth a try if you don’t want to spend too much money to get the audio into the Sonos eco-system.

Personally speaking however, I would have looked at adding a Sonos Soundbar, or Amp, instead, as those products can accept an optical connection (with or without an Optical adapter - depending on the chosen product), but it does of course mean a greater financial outlay, but it’s a much better, more-reliable A/V option.