RDS Farm. After the migration of the connection broker, clients can not longer log in under the old shortcut with the old broker inside.

Question

I have successfully migrated the connection broker RDCB1 and collections to a new server with a new ip address and a new name RDCB2. There was one problem left and I couldn't find a solution. Hundreds of users still have the old shortcut on their collection, which contains the old broker's name in its properties RDCB1. The solution to the problem is to go to RDWeb and download a new correct shortcut for collection from there or manually change the name to the RDCB2 in the shortcut, but I want everything to be transparent for users and they would not have to copy the shortcut to the collection again or changethe the shortcut manually. I tried to make an Alias of the old broker to the new one on the DNS server, but then the client had an Authentication error.