I assume that your son is an employee and gets a W-2 showing how much he was paid. Under current tax law (for 2018 through 2025) there is no special treatment for moving expenses for an employee. The money that the company paid is just additional pay. It should have been included in the wages on your son's W-2. If it was not, the company should have issued a corrected W-2 to include the moving expenses. Sending him a letter is a poor substitute for a W-2 or corrected W-2.
It makes no difference whether the company paid the mover or paid your son. All the money that they paid for moving expenses is additional pay and should have been included in his W-2.
Your son should first ask his employer for a corrected W-2 that includes all the moving expenses that they paid, both to him and to the movers. He can then file an amended return to make the corrections to the W-2. If the company refuses to issue a corrected W-2, he will have to file an amended return with a Substitute W-2, Form 4852, to show the correct amount that should have been reported as wages. If he is using TurboTax, he can create Form 4852 by checking the box on the Uncommon Situations screen in the W-2 entry section that says "Didn't get a W-2." (It also applies to an incorrect W-2.)
