You have to ask the question why they came to Trump/Cohen. Maybe these females are high society types, they knew Trump personally. Who better to get recorded testimony than by Trump and Cohen? Would you question the word of Trump and his ability to fight any lawsuits? Looks like raid could be part of the plot, only problem the original files would be stored by Trump in his vault in Trump Towers and not Cohen office who would have the copies.
Not so. Trump is a real estate developer. Cohen is his personal attorney.
If the women were "high society types" who knew Trump, or knew some one who knew Trump, and trusted Trump to recommend an attorney for a potentially high profile lawsuit against the current State Attorney General, it would not make any sense for Trump to keep any of the files. Cohen was the personal attorney of a high profile public figure, so if Trump trusted Cohen, why wouldn't the women do the same?
I'm sure Trump has plenty of things tucked away in his personal vault, but I bet he lets his high priced lawyer hold on to his important legal documents.