The following are the steps to take to alter the CID when dialing between extensions. The numbers used here are as an example. You can change them to whatever you need them to be when creating your own CID IVR.
Create an IVR called ChangeID
Create IVR actions
Alter CallerID "Replace CallerID # with 201
Set Variable 'test' = DIALED_NUMBER
Dial Extension from variable "test"
Create IVR extension 888 and assign it to IVR 'ChangeID'
Create a new outgoing call rule and set Number begins with (leave blank) the rest of the number must be between 3 and 3 digits in length (or 4 and 4 digits in length, depending on the extension scheme of your pbx)
Before connecting the call, trim 3 digits from the front, and prepend the digits 888.
Set Call through Primary Call through Provider Internal and set this rule as final
Set Allow all existing extensions to use this rule to NO and then save
Navigate to the Setup tab > Extension > Manage > Action > Modify 401 and go to outgoing call rules and remove the call rule Internal and assign your new call rule to extension 401.