I doubt this is a licensed "property management company."   The client is still doing business with them after the loss on the first property?  They must be exceptional salespeople.  

I would claim the operating expenses for the "rental" of Property A, on Schedule E.  Then I would claim the basis of Property B as whatever was paid for Property A.  The $10 amounts shown on quitclaim deeds is irrelevant.  Substance over form.  Taxpayer bought a property from the seller, with the understanding that it would make money.  When the first property didn't meet that condition, seller delivered a replacement property for the same price.