The bacteria that keeps your tank cycled lives attaches to surfaces... it exists in the rock and the sand and in filter media. There is very little, if any bacteria in the water column and reusing water from the old tank will do nothing to help the new tank cycle. Simply transferring your rock and filter media (if you use any) to the new tank will allow it to cycle immediately. You’ll need to make sure that the rock and filter media stays wet with salt water the entire time.
There is some benefit to reusing tank water simply because the fish and corals are used to the chemistry of that water... the salinity, pH, alkalinity, calcium level, etc. However, just getting the parameters as close as you can and using all new water isn’t too hard on the livestock either.
As I stated above, by transferring your rock you really shouldn’t see a new cycle, however, it would be prudent to keep a close eye on the ammonia level for a while after the move just to be sure that there was no die off or other issues. I might check the ammonia level twice a day for the first few days, then once a day for a week or two. You could also get one of those stick on ammonia badges to help keep an eye on it.