Your friend needs to tell her daughter, as unemotionally as possible, that she does not want her son in law to go into other rooms in her house without invitation, and leave her to deal with it as she will.
When the son in law visits again she needs to watch him like a hawk, follow him if he leaves the room, and again, unemotionally as possible, ask him directly if he is looking for something.
She also needs to check her possessions.
My uncle, many years ago, used to stay with my grandmother for brief visits and never went home without something: towels, travel blanket, old family papers, and his excuse was, when confronted, well, she never uses them, and I am her son. After he died and we had to clear his house, we were shocked at the amount of things he had accumulated, much of it actually belonging to my father. As a bank manager, one would have expected him to be a model of honesty.
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To think that London, or anywhere else for that matter, does not belong to any one demographic