CS, what an awful situation !
Can you get a mental health professional to back you up regarding the severity of your symptoms ?
I can't believe how difficult this is for you, after all you are not the only person on benefits that is homeless. I hope the PO box advice helps,you out. Maybe homeless charities may have some ideas for you?
Could you get your ex to tell them he made a malicious complaint regarding the fraud ?
I feel for you and hope it works out. Please take care and try not to get too stressed - you need a clear head to fight this.