Have someone else who can post on the FB page from a different state on an unsecure router? I ask, because the FIRST THING my WH's OW did when she got my email was contact the police and have them trace my IP#.
Don't know all the variables at play with your peeps, but just want to throw it out there that it needs to be an unsecure router (McDonalds has free wireless access; just check their website to find locations all over the States). Otherwise, if the police get involved, it could easily get traced back to you. If you have a friend or relative near the state where this new OM is and they trace the IP to a public location, no one will suspect you.
