The Exalate app allows syncing change history between JIRA Server Instances.

Issue change history is a list of change history items.

The change item includes several records, such as the person who made the change; the time at which the change was made; the new and old values of the field that was changed.

Please use scripts below to synchronize change history on JIRA Server. 

Source side

Outgoing sync

replica.changeHistory = issue.changeHistory

Destination side 

Incoming sync

 issue.changeHistory = replica.changeHistory