I've seen many things. But the unwritten encouragement given is to wait at least one year. The congo one is in gets the details if too far away from the disfellowshipping congo to facilitate a hearing. It then conveys those details along with it's opinion to the original congo. The original one makes the final decision. They have the case notes and generally do NOT forward those notes to the new congo. Elders are given training at KM school and extension classes at CA time as to how to proceed on specific issues that may have recently burned elders in the circuit or that may come from the branch office. CO's are rarely contacted unless they happen to be visiting or the case is unusual. They can go off of a first letter but many times don't as they want to be sure that you are "repentant".
Isaac