This article shows how you can set the remote issue key into a local custom field.
Exalate allows you to update the source issue automatically once the synchronization is finished. You can do that with the help of the syncHelper.syncBackAfterProcessing method.
Incoming Sync (destination side)
if(firstSync){
syncHelper.syncBackAfterProcessing()
}
Warning: Using nodeHelper.syncBackAfterProcessing() outside the if(firstSync) block might cause infinite loops.
Incoming Sync (source side)
issue.customFields."remote issue key".value = replica.key