3 speed ceiling Fan switch is broken. It is an Emerson SWQSRR Controller. My understanding is that Emerson no longer makes it.
I tried a Lutron 3-way fan control (Home Depot) DVFSQ-F but I can't get the middle speed which is the one we use 98% of the time.

How many wires is the Emerson controller, and does it control fan and light or just fan? Does it have a reverse button, or any other features other than just three speeds?

Ceiling fan remote controls - help and FAQ- Ceiling Fans N More

Can you wire up for Full Speed, and use regular Fan Control to give full range?

Strat this is a wall control he's referring to. I think it is computerized or RF.