RWY INCURSION AS A B737-300 FLT CREWCROSSES THE HOLD SHORT LINE AT TXWY M NEAR RWY 25R AT LAX; CA.

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AFTER COMPLETING AN HGS AIII PRACTICE APCH TO RWY 25L AT LAX; THE CAPT EXITED THE RWY AT TXWY M. AFTER LNDG; THE TWR DID NOT ISSUE THE CUSTOMARY HOLD SHORT RWY 25R CLRNC. ALTHOUGH THE CAPT APPEARED TO BE SLOWING TO A STOP; I NOTICED THAT HE WAS PREOCCUPIED WITH SOMETHING TO HIS L; AND WAS NOT LOOKING FORWARD. SO; I REMINDED HIM THAT WE STILL NEEDED TO HOLD SHORT; BUT GOT NO RESPONSE. WHEN IT BECAME CLR THAT HE MIGHT NOT STOP; I STATED 'STOP-STOP-STOP;' AND PREPARED TO STOP THE ACFT ON MY OWN. THE CAPT RESPONDED BY BRAKING; BUT THE ACFT ROLLED SEVERAL FT BEYOND THE RWY 25R HOLD LINE; COMING TO A STOP WELL SHORT OF THE RWY. TWR CANCELLED A TKOF CLRNC TO A DEPARTING ACFT ON RWY 25R; AND TOLD US TO HOLD SHORT. WE WERE LATER CLRED TO CROSS; AND GND GAVE US A NUMBER TO CALL. AFTER THE EVENT; THE CAPT EXPLAINED THAT HIS ATTN WAS ON THE HGS/COMBINER; AND DID NOT REALIZE THAT THE LINE WE WERE APCHING WAS THE RWY 25R HOLD LINE UNTIL I STATED 'STOP.' SUPPLEMENTAL 579547: I GO BACK AND FORTH FROM R TO L SEAT; SO I WAS TRYING TO KEEP UP MY HGS CURRENCY. AFTER LNDG; I STILL HAD THE COMBINER DOWN FOR THE HUD AS I WAS EXITING THE RWY. NEXT TIME AFTER LNDG; I WILL PUT THE HUD UP UNLESS THE WX REQUIRES IT.