In order to route a call that comes in a NETWORK TERM back out another (or even the same) NETWORK TERM entry then you have to configure the "Automatic Routeback Rejection" to DISABLED. This option is under DIAL PLAN and GLOBAL PARAM. It is ENABLED by default to prevent call routing loops between the ATLAS and the PSTN.
Under the NETWORK TERM, you will want to add the number you want to forward to the OUT#ACCEPT list. This should be the phone number that is presented to the ATLAS on the inbound call. In this case, the 503-111-1111 number. The OUT#ACCEPT should be how the call is presented, so if you are only receiving 4 digits, then the OUT#ACCEPT will only be 1111, but I will assume all 10 digits are presented.
After the number is added to the OUT#ACCEPT, go to the SUBSTITUTION TEMPLATE and set the "DNIS Orig #" to be the original inbound number presented to the ATLAS (503-111-1111) and the "DNIS Subst #" to be the number you want to "forward" the call to (503-222-2222).
Because of call routing,billing, and networks allowing calls only from specific numbers, you may have to go into the ANI template and set the "ANI Orig #" to be "$" and the "ANI Subst #" to be one of your 10-digit numbers (such as your main billing number, or the 503-111-1111 number).
This will use 2 channels on your PRI. One for the inbound call to the ATLAS, and the second for the outbound call from the ATLAS, but it should work.