We have set up a SIP URI connection in order for a third party to send calls to a 3CX system. The way it is set up, the calls come in to an extension which is set to forward the calls to a ring group. All phones in the ring group ring but the softphones stop ringing almost immediately while the Polycom desk phone continues to ring and is able to be answered and interacted with. I set up a softphone directly on the extension that forwards the calls so that I could test answering it directly and it also exhibits the same pattern, though one time I answered the call quickly enough to actually pick it up and interact with it. I have captured 4 calls (including the one that I was able to answer) in two separate PCAPs and can send for analysis. The Wireshark Call Flow analysis does show two lines that appear to cause the drop:
From this packet capture, asuming that the Left Column (sorry, no IP visible...) is the 3rd party sending the call, you see the INVITE arriving at the 21st second, ringing for ~13 seconds, then at the 34th second, the 3rd-arty instructing 3CX to stop ringing (CANCEL), assuming of course that 10.0.0.191 is your 3CX Server.
Personally I would suggest having your 3rd party send the INVITE messages and on the 3CX side, have a Generic SIP Trunk that would handle the incoming call and route it to wherever you want.
This is a non-3CX supported setup, so I really couldn't give you any more tips, just best-guess, but you can check here how SIP Trunks work in 3CX and configure the 3rd-party accordingly: https://www.3cx.com/blog/docs/voip-provider-interop-explained/
