Do they get a Cross tattoo when they convert? If not, then they can be whatever they want any day of the week. What is preventing them from converting back to Islam.
This should not effect their refugee status. If Merkel was smart, she would announce that conversion would not affect their refugee status and watch the conversions dry up.
Lying is a part of Islam, I am not shocked.
Offer them a pork sandwich during their interview by all women and see how it goes.