By third party...you mean another PBX? Passing the desired Caller ID across a 3CX Bridge trunk has always been an issue, depending on exactly what you want.
Perhaps if you include more information about what equipment you are working with, and the desired outcome.....
PBXs that are bridged to yours, can dial out via your trunks.
The remote PBX will not have any control though, but if you have an outbound rule that allows the remote side to call out, outbound rules now have the ability to define an Outbound Caller ID