ZLA Controller described a TCAS conflict event reported by a LAX Air Carrier arrival; traffic was issued and sighted by the suspected conflicting aircraft.

Narrative

I was at ZLA R13. There were strong winds from the northwest requiring LAX arrivals to cross SYMON at 12;000 FT and 250 KTS. Due to this restriction LAX arrivals were lower that usual. A C340 checked on my frequency from ZUMA heading northwest; VFR at 12;500 FT. I issued him the BFL altimeter. I issued traffic to the C340; a heavy B777 descending via FIM for LAX. The C340 was indicating 12;300 FT and the B777 was indicating 14;700 FT and approximately 10 miles. The C340 said he was looking for the traffic. I instructed the C340 to turn 10 degrees right for the traffic. The C340 informed me that he had the traffic in sight; leading me to believe it was no factor. At the same time an aircraft called; which because of the difficult accent; I thought was the B777 checking in. I issued a clearance to the B777 to cross SYMON and then issued a frequency change. When the B777 informed me of the TCAS alert two aircraft transmitted at once. I reissued the frequency change to the B777; the pilot then then informed me they were filing a near midair on the ground. The B777 was descending into ZUMA's airspace with multiple targets for LAX. I acknowledged and reissued the frequency change again. I immediately informed the Supervisor of the incident.