A FA50 CREW WAS GIVEN A LATE LAS ARR CHANGE TO THE TYSSN 2 10 MILES FORM THE FIRST FIX. THE CREW WAS BEHIND PROGRAMMING EFB'S AND THE FMC'S.

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ENROUTE FROM ZZZ TO LAS; I WAS ON COM ONE OBTAINING THE LAS ATIS WHEN CENTER CALLED THE CAPT ON COM TWO AND CHANGED OUR ARR FROM THE KADDY 1 TO DSND VIA THE TYSSN 2 ARR. WE WERE ONLY 10 MILES FROM THE INITIAL ARR FIX WHEN RECEIVING THE CHANGE. I REPROGRAMMED THE FMS TO THE NEW ARR; WE THEN REALIZED THAT WE COULD NOT MAKE THE CROSSING RESTR FOR THE FIRST FIX. LAS ATC ASKED ME WHY; AND I INFORMED HER THAT ATC HAD SWITCHED ARR ON US AND I DID NOT HAVE TIME TO GET ALL THE CROSSING RESTRS IN THE FMS FAST ENOUGH TO MAKE THE DSCNT. AFTER THE MISSING THE FIRST CROSSING FIX; WE WERE THEN TRYING TO CATCH UP WITH THE CHKLISTS AND REPROGRAMMING THE BOTH FMS. I FINALLY FOUND THE NEW ARR ON MY EFB; AND WAS STUDYING IT WHEN THE CAPT SAID PRIMO AT 8000 FT; TO I AGREED AND SET IT IN THE ALTITUDE ALERTER AND THE AIRPLANE STARTED DOWN PREMATURELY. ATC NEEDS TO GIVE THE CREW MORE LEAD TIME WHEN CHANGING ARRS; AS IT TAKES TIME FOR THE CREW TO REPROGRAM THE FMS COMPUTERS; AND EFB'S. THE CREW ALLOWED ATC TO RUSH US THRU A PROC THAT WE WERE NOT READY FOR.