a hard set of rules for re-instatement that is in a publication somewhere, or do re-instatement rules vary from place to place
From Organized to Do Jehovah's Will (internal procedure manual), pages 156-157:
A disfellowshipped person may be reinstated when he gives clear evidence of repentance, demonstrating over a reasonable period of time that he has abandoned his sinful course and is desirous of having a good relationship with Jehovah and His organization. The elders are careful to allow sufficient time, perhaps many months, a year, or even longer, for the disfellowshipped person to prove that his repentance is genuine. When the body of elders receives a written plea for reinstatement, the judicial committee that disfellowshipped the person should, if possible, be the committee that speaks with the individual. The committee will evaluate the evidence of works of godly repentance on his part and decide whether to reinstate him at that time or not.
If the person requesting reinstatement was disfellowshipped by another congregation, a local judicial committee may meet with the person and consider the plea. Thereafter, the local judicial committee will communicate with the body of elders of the congregation that disfellowshipped the individual, giving them its recommendation. The involved committees will work together in unity to ensure that all the facts are gathered and a just decision is made. However, the decision to reinstate is made by the original judicial committee of the congregation that took the disfellowshipping action. If some members of the original committee are no longer in the congregation or qualified to serve, other elders from the original congregation can be chosen to replace them.
When the judicial committee is convinced that the disfellowshipped person is genuinely repentant and should be reinstated, an announcement of the reinstatement is made in the congregation where the individual was disfellowshipped. If the person is now in another congregation, the announcement will be made there as well. It should simply state: "[Name of person] is reinstated as one of Jehovah's Witnesses."