Hi There
It is not very clear to me from your posting exactly what you are trying to achieve.
You state that you want to configure Router A to send all traffic to the IP address 1.1.1.1/24. Is this IP address assigned to a remote routers interface, directly connected to Router A?
Or is this IP address on assigned to an interface on Router B?
If the IP address 1.1.1.1/24 is assigned to a remote routers interface directly connected to Router A, then you can configure a static deafult route to send all traffic to this address.
However if the IP address 1.1.1.1/24 is assigned to an interface on Router B, then IMHO the answer would be No, this would not be possible as there are multiple routers between Router A and Router B which are outside of your control, unless these routers are all under the control of a single entity (SP) and the (SP) would configure static routes for you to get all traffic from router A to pass through router B.
However this would not be an easy topology to support and troubleshoot.
Just my 2 cents worth.
Best regards,
Michael