If an external call is forwarded to another outside number, typically the caller ID would show either;
A) the caller's Caller ID presented as outgoing caller ID
B) the default caller ID as specified under Trunks - Calling Number.

If you have number verification enabled, then the outgoing caller ID should be the default caller ID

For extension's caller ID on outgoing calls usually I set this under Trunks - Caller ID instead if the Station's Network Calling number