If it’s an IR remote, then you can use the Logitech Harmony hub and the fan will just treat it as another remote. But if it uses 334 MHz, 443 MHz, or some proprietary frequency, then there’s no easy way to do it.
You can check the harmony database to see if the fan is listed:
But I think most of the Hampton Bay fans are unfortunately not using IR remotes.
There is a zigbee remote that is compatible with many Hampton Bay fan models and that works well with SmartThings, but that one would require rewiring both the fan controller and the wall mount remote.