Moving a central administration site to another sever in the same farm is essentially a two part process. Part I, where all the steps are performed in the source server (current server hosting your Central Administration website) and Part II comprises of steps to provision new Central Administration site on the destination server (future home of Central Administration site).
Part I
Step 1) On Source server, run the products and configuration wizard.

Click on Next > button.
Step 2) Click Yes to the following screen.

Step 3) Ensure that you have “Do not disconnect from the server farm” selected.

** Do not select “Disconnet from the server farm” This will essentially delete all the web applications, which is probably not something that you want.
Step 4) Select “Yes, I want to remove the website from this machine”. This step is really important.

Step 5) Ensure that “Host the central Administration web application” is showing status = “no”.

This completes the part 1 of moving the central administration site to another server in the farm.
Part II
Now, log in to the “new” or destination server that will host the Central Administration site. Run the products and configuration wizard.

Step 2)
Ensure that you select “Do not disconnect from this server farm”

Step 3) Now, provide your preferred port number and Authentication methods.

Click Next.
Step 4) Ensure that “Host the Central Adminsitration Web Application” shows “Yes”

A
At this point the configuration will start.


That’s it. You have successfully moved your Central Administration site to another server.