in theory a Bluetooth transmitter/receiver pair could connect through optical to the Beam but:

• it would only be in PCM stereo, not DD5.1 or better
• quality would be compromised by the lossy Bluetooth codec(s)
• a substantial delay would be inserted into the audio, potentially ruining lip-sync

You might be able to improve things with a proprietary lossless, low latency, wireless transmission of some kind but IMO the endeavour is unlikely to yield satisfactory results. 

Thank you for the suggestion  ! I could try Avantree Bluetooth receiver with aptx low latency:

Avantree TC417 Bluetooth Transmitter Receiver for TV, Optical Digital Toslink, Volume Control for 3.5mm AUX, RCA, 20H Playtime, aptX Low Latency Wireless Audio Adapter for Headphones, Home Stereo https://www.amazon.com/dp/B07JJCZ3WL/ref=cm_sw_r_cp_api_glt_fabc_9XTRBWHJTWVZTKVQF2GT

Also after so much of research to get beam to work wirelessly with projector, I think I am ready to settle for PCM stereo with a little bass. I am currently using Alexa echo speakers, better than that.

I anyways need to choose between 50ft hdmi cable vs Stereo sound. 

PS : Sonos beam is an amazing soundbar. I am going to keep it. So am ready to do a lot of adjustments for that. But I really wish Sonos had a use case/ solutions for long throw projectors other than running a long cable.

Even aptX low latency will add 30-40ms, plus there’s ~30ms in the Beam itself. At 60-70ms in total you could well notice a loss of lip-sync. 

Ok. I currently use an Alexa echo dot speaker through bluetooth and there is literally no noticeable lip sync issues when connected to firestick 4k. I will reply with results, no harm in trying.

If you would decide not to go for the bluetooth option, check if your projector is equipped  with HDMI-ARC (or eARC). The Beam needs it, but I do  not see it mentioned here: https://www.lg.com/us/home-video/lg-hu70la

When the projector does not do HDMI-ARC, you could go for an optical cabel (no Atmos though, but you'd loose that with bluetooth too). 

@106rallye … The projector has HDMI-ARC port. I did check that. But this projector is suitable for ceiling mount and to connect to sonos beam, I have to run a 30ft hdmi cable from projector to beam. I want to avoid such a big cable.

Result : I got Sonos beam to work with below Bluetooth adapter. :)

Avantree TC417 Bluetooth Transmitter Receiver for TV, Optical Digital Toslink, Volume Control for 3.5mm AUX, RCA, 20H Playtime, aptX Low Latency Wireless Audio Adapter for Headphones, Home Stereo https://www.amazon.com/dp/B07JJCZ3WL/ref=cm_sw_r_cp_api_glt_fabc_9XTRBWHJTWVZTKVQF2GT

I am happy with the sound output as such, but definitely not as good as Dolby digital or Atmos. But I am glad I have a bluetooth enabled Sonos Beam. My purpose was to avoid a long cable and that is achieved.

I recently got a Sonos Beam soundbar and (unfortunately) realized it doesn't have Bluetooth support to connect to my projector. I am willing to keep it because I've heard about the sound quality but it is a bit frustrating.

Regarding the Bluetooth adapter above, how did you connect it to the Sonos? As from what I can tell, it only has HDMI and LAN wire output... And then you simply connected your Projector to your Beam through Bluetooth right?

Cheers! 

Just connect the hdmi to optical cable that comes with sonos soundbar to the spdif out port of the avantree bluetooth adapter as shown in the diagrams above. The other end of the cable with hdmi will directly plug in on sonos. Set the Bluetooth adapter to Rx mode. 

Ah right I missed the adapter connection was HDMI, thanks, will definitely try it i guess... No other options!