it still stands when you move, but as star says, an emergency review can be called, or new LA might just wait for annual review, if not too long.
I think, star, that the rest of what oyu said depends on what LA you are moving into, and what is written into your statement.
eg we have won dd1's statement. full time ABA school, out of county placement.
ironically, we own a house in the county that dd1's school is in (we used ot live there, moved ot present LA for dd1's last school) but we cannot moveback there, and are stuck with the longer commute, etc.
if we moved back, new LA would certainly challenge, bacuse they have recently opened a new provision for ASD, which has notbeen proved unsuitable to meet dd1's need. just because we proved that where we are, doesnot mean that that argument holds for new LA.
new LA can and do re-open statements for this very reason - they have retained a lawyer purely to fight ABA cases (used ot fight ABA for the parents until LA offered more money) - they have already doen so, and won, removing ABA since the new provision opened.
of course, it would be a matter of time, in our case, becasue we would fight and re-fight, but it would also be wastedyears of dd1's education, and damage done in the meantime.
so, basically, the arguments oyu use ot win provision in one county cannot necessarily be carried over - each LA's provision varies, and it is up to the parents, as ever, to prove that what the LA is offering is unsuitable. often this involves trying it and proving it fails.