Welcome. My name is ***** ***** would be glad to assist.
Looking at the specifications, the 85612 has the small slide switches to set the frequency to match the receiver and remote together.
The receiver is built into the fan itself and not in the canopy at the ceiling.
The 99110 remote does not use slide switches, but pairs with the fan directly through its receiver similar to a garage door opener. It has a receiver that mounts in the fan canopy at the ceiling.
So, unfortunately the two are not interchangeable.
You cannot install a receiver in the canopy area at the ceiling when the fan uses one internally.
You will need another 85612 remote or receiver depending on which is bad?
The remote or the receiver part inside the fan
The 85612 is still available from Hunter--CLICK HERE
Or you can contact the company--CLICK HERE and they will most likely have the remote to match the 85612 receiver
They have the most extensive inventory and access to fan parts.
Let me know anything further needed, just reply