I agree Brian. I'm a network engineer as well, and uh, even if they find the router, unless it's logging itself to flash, they won't find any evidence. Maybe if it's configured for voip that's some pretty pressing evidence.
I think if they want to find out where the call came from, the "stolen router" isn't the key to the technical piece of the investigation. The routing of the phone call is. It would be routed through the telco system a certain way, and if he did fake it, the origin of the call would be the server where the voip client (router or otherwise) was registered, and not his wife's cell phone.
A subpoena to the telco in question would yield better evidence and the router config, or the router itself would become a moot point.
It's a network. The tracks through the network are the evidence, not any single piece of equipment.