At the risk of sounding like your grandmother, honesty is the best policy.
If I have understood the facts correctly, your wife travelled on your season ticket. Season tickets are not transferable, so that means that she has committed an offence.
It's not clear if she did it with your knowledge. If you did know that she was going to do it, then you have also committed an offence.
If your wife sends in details of a new photocard, then unless she explains precisely when she obtained the new photocard, the railway company could interpret this as an attempt to mislead them into thinking that she had the right to travel on the ticket that she showed. That would not make the situation any better.
My opinion (and like most of the people here, I am not a lawyer) is that since your wife has been given an opportunity to make contact with the railway company, she should take it. As has been explained in posts above, since the ticket was a season ticket, the railway company might argue that just because this was the only occasion that your wife was caught not paying her fare, it doesn't mean that she has not done it before. So (assuming that this was a one off) if you can produce evidence that your wife always pays for this journey (e.g. old railway tickets, entries on a bank/credit card statement showing purchases of a ticket at the right price) or has never previously had cause to make this journey (e.g. until recently she was working somewhere else that she would not reach by train, or had a bus pass etc.) it would be good to do so.
Your wife is unlikely to come out of this without having to pay something. The very least is the fare for the journey in question - and that would be an unprecedentedly good result. On the basis of previous cases discussed here, the least that the railway company will want is the cost of the fare not paid, and the cost of their investigation - which will run into hundreds of pounds. Or they may seek prosecution - which if successful would involve your wife paying a fine, compensation (the train fare and any other fares that the railway argues to the court's satisfaction have not been paid), court costs and the prosecution's costs.
As (per your original post) there is no doubt that your wife has committed an offence, I don't think this forum can recommend trying to duck her responsibility. The best your wife can hope for is that the railway company will not be harsh: the best way to encourage the railway company is to fully co-operate and be totally open.
One last point - something like this can put a huge strain on a relationship. Both you and your wife need to be aware of that, and work hard to support each other to deal with what will inevitably be a difficult experience.