This ain't hard, just show them the transactions you've made via Blockchain and your wallet history that you are not the thief but just a victim. However, it may be hard to convince them since authorities are not familiar about how cryptocurrency works, and paying that 2 Bitcoin in cash is insane especially if the thief deposited it on an exchange to set you up (if it is intentional), I'm only confused about all of this.

I mean why spend 1 year on that case if it can be proven instantly with all that transaction history, right?