If they cannot document it as a service animal, then they submitted a incomplete application.
IF you fear a lawsuit before they move in, just imagine your lawsuit when they do move in and you are in their control.
Get rid of your PM. I have had people threaten to sue me for discrimination but I remind them that there are protected classes. Criminals are not a protected class. Pet owners are not a protected class. I would tell the prospective tenant that I will continue to take complete applications until it is rented. If they do not have the proper paperwork to verify that it is a service animal, than it is considered a pet. You can discriminate against pets. I require a prescription, to verify a service or Emotional support animal. Without it, it is just a pet. Alot of people threaten to sue but most don't have the money to get a lawyer to find out they don't have a case. Bottom line, get rid of the PM. Give your PM 30 days notice and find a new PM to take over. Personally, I would find a more qualified renter. Let them spend thousands of dollars in lawyer fees to find out you choose a different qualified renter.