Legal Question in Wills and Trusts in California

You don't record deeds in court; you record them in the County Recorder's office (in some counties, these are in the same building.) And yes, if you are acting under the instructions of the grantors, you may record the deed for them, either in person or by mail, if accompanied by a Change of Ownership Report and with proper fees enclosed.

N.B. if the transfer is from parent to child, be sure to also file a Claim for Exemption from Reassessment