Being robbed is so disconcerting. There's a lot of that going around these days. Such a violation - whether it's done by a family member or by some unknown perpetrator. I'm assuming you reported the breakin to the police and to your insurance company, so you've really done all you can at this point.
I think detective work will drive you crazy. Even if the button doesn't match, it doesn't mean he didn't break into your house. And if the button does match, it really isn't enough evidence to convict him of the crime (or in our own minds - deny deny deny is the motto of every addict). It's never enough really...
Prayers for you that you are able to hand the situation over to your higher power, enjoy your lunch, let go and find some relief no matter what the outcome.