By “ping” I assume that you mean an ICMP echo request (what the ping command in Windows, Linux or the phone’s command line does).
A router normally does not forward ICMP but handles it internally, so when the MN phone pings the CO PBX on its public IP address, it’s actually the router that is answering. However, a ping from the CO phone must be answered by the PBX and a firewall may be blocking that.
Can the CO phone ping the router’s LAN address? If not, check the network settings. If that’s ok, can the PBX ping the local phone? If so, a firewall is likely blocking the other direction (and also likely blocking SIP). Possibly, https://www.raspberrypi.org/forums/viewtopic.php?t=98936 may help. If not, post details about FreePBX version, OS version, etc.
What log file in what device? Normally, a ping wouldn’t cause anything to be logged.