How to get true end-to-end CDR records with call group?

When we get an incoming call that is picked up via a simple ringall Ring Group, the standard Asterisk CDR destination field (dst) contains the ring group number instead of the end user extension that actually picked up the phone. This is too bad because we want to know who actually spoke with the external caller.

Is there a way to change this behaviour without patching the code?

We are using AsteriskNow 1.7.1 with FreePBX updated to 2.8.1