From Calguns Wiki

Shipping Firearms Within California

In some cases no FFL is required for a transfer of firearms, so shipping may be done between two unlicensed individuals

Transfers of firearms between a father and son are exempt from California's FFL transfer requirements. Transfers of firearms between two unlicensed residents of the same State are exempt from Federal FFL transfer requirements.

Handguns need to be shipped via UPS or FedEx. Unlicensed people can not ship handguns via the U.S. Post Office. UPS and FedEx both require that handguns be shipped via their "next day/overnight" services. This might cost you around $60. UPS company policy allows an unlicensed person to ship a firearm to another unlicensed person as long as all Federal, State, and local laws are followed. You might run into problems with UPS employees not knowing this. FedEx company policy does not allow an unlicensed person to ship a firearm to another unlicensed person. You might get lucky and have the FedEx employees not know this.

Long guns may be shipped via the USPS. See the Domestic Mail Manual, 11.1

You have to ship firearms either from your daily pick up account or by going to an actual UPS or FedEx customer counter. "UPS Store" and "FedEx Kinko's" franchises are not allowed to accept firearms shipments. Both UPS and FedEx company policies require that you notify them that you are shipping a firearm. Federal law does not require you to notify the carrier if the firearm is being shipped within the State.

With a grateful hat-tip to Mssr. Eleganté at Calguns.