Of course, center can you clear one for an approach, as an OAC can, IF it has control of the airspace. The airspace at KPOC is controlled, normally, by SoCal, so KZLA cannot issue an approach clearance to an aircraft in its airspace that would then exit it's airspace I to SoCal airspace, except with coordination with SoCal or a hand-off to SoCal with a frequency change.
My background is posted, I don't fly the Jet Commander Mode 10. The Galaxy is a Lockheed Georgia product.
GF
Are you SSG V10?