The only way I can think of that would allow you to record these calls would be to utilize the "Ring my mobile simultaneously" feature.
If what you have currently is the Queue "Destination if no answer" setting set to "Forward to Outside Number", you would have to:
1. Create a dummy extension.
2. Set it's mobile number to that of the Outside number.
3. Edit the extension and go to "Forwarding Rules >> Available" and enable "Ring my mobile simultaneously".
4. Also go to "Options" and enable "Record All Calls", then to "Phone Provisioning >> 3CX App" and enable "Show Call Recordings".
5. Go back to the Queue and set the "Destination if no answer" of the Queue to be the dummy extension.
Calls will now be routed to the dummy extension that will then ring the external number. These calls should be recorded and the owner of the recordings will be the dummy extension.
Let me know if you have any issues with it.
