Bear with me here, for a different angle:
So far, no-one's mentioned the fact that the child's mum found the money in his pocket -and immediately contacted her ex- to ask about it. If she was just out for stealing, why wouldn't she just have pocketed it and asked/said nothing?
Maybe she asked because if it came from school or a friend, she would have returned it. Maybe she hasn't t returned it because she's got some stored up anger against her ex or believes he owes his son? (OP's referred to court cases etc, we don't know the background). Not saying this is right of course, just wondering if it's a potential explanation for the crazy "in an unbreakable piggy bank" story (I love the comment where a PP says 'she knows it doesn't have to be the original twenty note, she can give any note back right?') If she's telling the truth about the unbreakable piggy bank, it suggests she's keeping it for her son (again because she might believe he's entitled to it). Please don't flame me, I am not saying her keeping it for herself or for her son is right, but I do wonder if there might be some benefit to looking at things from all angles here.
One thing -- OP has referred to "my child" three times now. Is her partner her child's father? If so, "my child" is DSS's DSB? Even if he's not genetically related, he's still DSB isn't he? The emphasis on "my child" is a bit "othering" for want of a better word. Does DSS pick up on this "my child" vs. "my partner's child" and is it hurtful to him? He last stole on "my child's" birthday. Was he feeling left out and sad?
I ask this because to me, a 7 year old stealing money like that, how is he going to spend it? Is he really stealing for himself because at 7, he's a thief, or bad genes like the OP says, or is he acting out in the way young children do, and does this acting out need dealing with in terms of underlying causes as opposed to action-consequence (remove the electronics vs trying to get to the bottom of why he did it)?
I'm probably too much of a bleeding heart but I think of this little kid taking something from his DSB's (genetic or not) birthday, and getting into a lot of trouble (=attention) for it, and then doing it again a year later (when is the birthday actually, OP, is it soon, is it being planned for etc?). OP's painted a picture of an atmosphere that is likely tense at home, the court case, the family money trouble's because of OP's partner's loss of hours, her own stress. Kids pick up on it all.
Sorry OP for your stress in general and over this. I don't mean to cast aspersions on anything you've done or said, but maybe just wonder if a bit more attention to your DSS's feelings might prevent a recurrence?
As for the mum, well, I'd buy another unbreakable piggy bank, fiver off amazon etc, and ask for the first one to be broken so your DSS can bring the money back and give the new one instead. I know you shouldn't have to spend the fiver but you'd make the point with her that you're not going to be a pushover, now or in the future.
At the risk of some godawful flaming I might also try to have a civil conversation with her and ask her why she's set on keeping the money, since it seems so clearly wrong. If she's got no rationale at all, and it seems opportunistic trousering, at least you've modeled civil behaviour.