I think many will acknowledge that I am quite critical of BA's systems and organisations to say the least, but in this particular case, I have to point out that to my knowledge, regardless of the airline, the fraud teams are never directly reachable (it's more than not customer facing, it is actually impossible to reach out to directly which is different). It's always a case of them reaching out to you if and want they need to or have a conclusion to deliver.

I think that in this case, this is not about money or service, it is about purpose. Fraud teams are not there to serve and protect the customer, they are there to serve and protect the airline, some times regarding massive amounts. The idea is to prevent risk of intimidation, corruption, influence etc and ensuring that investigations happen in as effective a way as possible, be it externally or even internally.

The customer facing route is the same as usual (ie you can call customer service), but it will know nothing, have no way of discussing with those who know, and will tell you that. And that is basically it. There is no "customer service" to be had because from the point of view of the fraud team, the passenger is not the customer. Here, we obviously all know of the OP as a victim, but that is not the way the fraud team will operate. For them, the victim is the airline, they know that something untoward has happened and they are trying to figure out what and how. In due time, they will undoubtedly reach the conclusion that the OP is a second victim here and return the avios, but that will be a conclusion, not a starting assumption.