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>>any subsequent changes in either of the DHCPs are not replicated to the other automatically.
Based on my knowledge, you can use the DHCP Failover Auto Config Sync.
DHCP Failover Auto Config Sync is a PowerShell based tool which automates the synchronization of configuration changes.
You can download the tool and usage guide from this post on TechNet Script Center.
Please refer the following link about more details:
Best Regards,
Candy