Surviving Parent giving consent to a family member for custody (child lives in a different state)
2 attorney answers
I am actually licensed in both States although inactive in Ohio. Years ago when I volunteered for court appointed work, I did represent persons charged with felonies for lying on government applications regarding the other parents whereabouts. Also if the non-custodian parent knew about the fraud he/she and was part of it, he/she can be charged with felony and held responsible for back payments. If you are interested in hiring an attorney - feel free to call Attorney Sheryl Shane. 703 582 8119.
Perjury is a Class 5 felony in Virginia. § 18.2-434. If OH prosecutors are checking, then there might be some Fraud charges pending when mother applied for benefits based on false info. Check with OH state lawyers.
Please note that my answer is general advice only and no attorney-client privilege attaches. It is a simple free "internet answer" and is not a clear substitute for retaining an Attorney for your case's resolution. Good luck.