Closing Costs if Someone Refinances, Only to Take Relative Off Mortgage?

refinances

My ex husband bought a house recently with the help of my son in law. He is now on the mortgage and wants off so he can get his own house. My ex has been told after he makes so many payments on time, he will be able to refinance. Someone mentioned a “quick claim deed” for my son in law and then my ex refinancing to take son in law off mortgage. Will this work? Is there additional cost to the ex for the closing?