B737-300 CREW USED CAPT'S EMER AUTH TO AVOID PENETRATING A TSTM.

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ON DEP; CLBING THROUGH 17000 FT FOR FL230; WE ASKED ZAB FOR A WX DEV OF 30 DEGS L. THIS WAS APPROVED. SIGMET WERE VALID AT THE TIME; RPTING TSTMS TO FL440 WITH ASSOCIATED RAIN SHOWERS AND CONVECTIVE WX ACTIVITY TO THE S; E; NE; AND N OF TUCSON. WE THEN ASKED ZAB FOR A FURTHER CLB CLRNC TO FL310. ZAB NEXT INSTRUCTED US TO COME L HDG 020 DEGS (A 270 DEG L TURN). THE CAPT REPLIED THAT WE WERE UNABLE AND THAT THAT HDG WOULD TAKE US DIRECTLY INTO THE WX CELLS TO THE E. ZAB NEXT STATED THAT ANY FURTHER DEVS L OF COURSE WOULD TAKE US INTO THE RESPECTIVE MOAS; WHICH WERE ACTIVE (R2304/R2305). HE THEN STATED THAT THE ONLY WAY WE COULD PROCEED INTO THE MOAS WOULD BE TO DECLARE AN EMER; WHICH THE CAPT SUBSEQUENTLY DID. THE CAPT ADVISED CTR THAT WE HAD 3 1/2 HRS OF FUEL; 121 PAX AND 5 CREW MEMBERS ON BOARD. ZAB NEXT ADVISED US THAT WE WOULD HAVE TO EXIT THE MOA TO THE S INTO MEXICO. THE CAPT ASKED FOR GBN OR TNP BUT WAS CLRED INSTEAD TO PUNTA PENASCO (PPE) DIRECT ALTAR DIRECT JLI FOR THE PDZ 4 ARR. WE SUBSEQUENTLY LANDED ON TIME AT LAX WITH NO FURTHER DEVS.