Exchange will eventually replicate the existing self-signed cert to the new Servers.
Just give it a few days. If you dont see it after that, do an iisreset and/or reboot the new servers and wait some more.
If they certifcates aren't replicating, that tells me you are blocking firewall ports between these sites which is isnt supported for Exchange Servers
We do not support restricting or altering network traffic between internal Exchange servers, between internal Exchange servers and internal Lync or Skype for Business servers, or between internal Exchange servers and internal Active Directory domain controllers in any and all types of topologies. If you have firewalls or network devices that could potentially restrict or alter this kind of internal network traffic, you need to configure rules that allow free and unrestricted communication between these servers: rules that allow incoming and outgoing network traffic on any port (including random RPC ports) and any protocol that never alter bits on the wire.