How do I go about settling this problem?

So a while back I stayed at my girlfriends house for a couple days because of an argument I had with my mom. Those couple of days went great! Or so I thought. One of those nights I was fixing their desktop computer, and doing some finishing touches, and I had my girlfriends laptop next to the desktop because I wanted to listen to music without worrying about slowing down the desktop PC so that I could get what I was doing over with. Everyone was asleep, so I needed headphones. I opened a drawer on the desk, and went through it to look for some headphones. As I was doing so my girlfriends mom came out to get some water and came across me looking through the desk drawer. She said nothing at the time, so I wasn’t worried.

A week goes by, and I get a text from my girlfriend saying that she was breaking up with me because she was told by her mom that there were fraudulent charges on her step dads credit card. Her mom automatically suspected it was me. She assumed while everyone was in bed, I snuck around looking through the drawers stealing information from them. The same day her mom caught me looking through the desk, I cleaned it, dusted the computer and organized everything on the desk and I vacuumed. It was pretty messy. There were papers that were apparently important on the desk, I had no Idea, I just put them all in a manilla envelope i found.

She used the night she came across me looking through a drawer, and the fact that I cleaned the desk as evidence and proof that I did it.

I have tried talking to the mom, but she just thinks I am a liar and a thief. I was blown away! I have never been accused of something so serious in my life. I also kept telling them to get netflix and get rid of cable because I knew they were tight on money. Guess what was on the credit card! Netflix, Itunes and a bunch of other things that my girlfriend told me. Why would I get Netflix? Why would I use itunes? Number One I use my moms netflix account, and number two I torrent all my music. My mom has had her credit card stolen. So I know how much it sucks.

It took a while for my used to be ex and now girlfriend to believe me. I now work at the same place as her step dad. I want to make things right! So how would I get around to starting the conversation to having him realize it wasn’t me. I know it doesn’t make sense that they didn’t contact the police. Thank you!