Not being able to swallow near the end of radiation and for days after is common with many patients. This is why a feeding tube is often recommended.
Myself I could only get liquids down. I also spent several nights sleeping upright with a large spoon in my mouth to keep my airway open. I’m fine now but everyone is different.
Are his doctors aware of the swallowing issue?

@phyllisg you and your husband are right to be concerned. Please ask about therapy for swallowing as this is usually done by a speech therapist. Your doctor can make a referral. Also remember that nerve tissue is very slow to heal, so damage done by surgery can take months to years to heal. My facial nerve was severed due to tumor involvement and while it was reattached, the nerve fibers don't heal and grow together quickly. At 5 months after surgery the doctors could tell that there was a little muscle tone returning but I saw no change yet. At 7 months I could see slight improvements in moving my tongue and a twitch of muscle when smiling. It continued to improve and change over the next 12 months and changes still happen now 12 years after surgery. Not using my face muscles by not talking and smiling and changing facial expression make me lose some of the muscle tone and strength so then I double up on my exercises. Learning the proper exercises with therapy will help him to keep what function he has as the nerves heal. Don't give up hope, this is a slow process. Ask about therapy.