Hunter Ceiling Fan Model #: 21871
Harbor Breeze Universal Remote Model # 43147

The Ceiling Fan has:
The black & white wires for the motor,
And red, pink, yellow & gray wires

The Remote has:
The black & white wires for the motor,
And ONE blue wire for the lights

How do I wire the fan to the Remote?

Connect receiver to black and white. Find the colors for high speed operation, connect to receiver.
Blue will go to receiver for light.

Ok, are you attempting to replace the remote receiver that came with the fan with the new Harbor Breeze receiver?

In addition to my earlier post, Or hopefully more clearly.
Black and White from ceiling go to remote black and white. Would think black, white and blue would be to fan and light wiring.
Red, pink, yellow and grey sound like fan control. Leave wires , put switch on Hi speed, on fan.
And control from remote.

I do not think you are correct, but I have not seen everything.

Ceilingfanrepair, sometimes I will address or say things to get them(The asker) to elaborate. Some of these are difficult, as you know. I am new here, and I appreciate all the help you give these people. I almost want to say. If it is a fan problem, Go to your sites you recommend, and info you provide. Most problems would be solved there.
Thanks.