My mother falsely claimed me as a dependent on her SNAP benefits ~3 years ago. I received an over payment bill for $~3600. What can I do?

Hi,

Bit of a stupid situation from my less than intelligent mother. I have been living by myself since moving out in 2009 after graduating High school. I went to college and got a 6 month internship in the fall of 2012. Internship was paid and paid pretty well ($18/hr). Very recently I received a letter from the Oregon Department of Health Services saying there was an over payment of SNAP benefits to my family (Case name is listed as my Mom, but letter is addressed to me). This is because during the period I was working on my internship my mother still had me on her SNAP file.

It wasn't an honest mistake on her part, she fed me some lines about how she needed more money for the rest of my siblings (another who was 18, but not working at the time). Obviously the government was going to figure out about this considering all they had to do was correlate tax returns and other information.

The bill says I am liable for this $3600 as well as anyone else on the case (in this case its me, my mother, my step father and my younger brother).

My mom can pay back the $3600 herself, she has agreed to do this. I am mostly concerned about side effects from this over payment action that might affect me (or my other family members) in the future. Will this hurt my credit? Will it show up on background checks and other things?

Was considering posting to r/legaladvice, but my concerns are more financial than anything at the moment.

Any advice at all would be very appreciated.

EDIT: I contacted the DHS and let them know that I have not lived with mom during this period of time and have a hearing appointment in place.