Same Cloth simulation for two sections

Hello,
I am doing cloth simulation on my cape and have a problem with one of them.

The cape is composed of two different material (fur arround the cape in red and main cape material on the middle in orange) :

(Here I apply random mat)

The problem is with cloth simulation. If I apply cloth simulation to them separatly, then they move separatly… And I want to keep the fur and cape attach together…

How can I apply the same cloth data to both fur and cape and make them move together ? Is there a way ?

I can’t just merge the material, it is the main problem…

Thank you a lot for your help !

All the best

I had the same problem, Have you found a solution?