We know that the shaliach tzibbur must follow the local custom even to the extent of his own silent Amidah .
What should be done, then, when a resident of Israel who is acting as shaliach tzibbur outside of Israel between 7 Cheshvan and 4/5 December, already said “vetain tal umotor”in the repetition of the amidah?
It seems to me that he must correct the mistake; is that right?