Agreed, Jed.
Address the safety, productivity, appropriateness of checking out of work all the time to go off into a virtual world. I have to suspect Walmart doesn't allow cashiers to stop working when their phone dings.
You have to set the standard for him to live up to. He will decide what to do. Across the crew (the company doesn't have a policy?????), no phone, X is the across the board disciplinary action for the first offense, Y for second offense, Z for third offense. Tell the crew what and why.
Jed you aren't firing the grown man, well past old enough to go to war and kill and die, the grown man is firing himself.
If it does come to it, and he goes, you're opening an opportunity for someone who does want to work and take the job seriously.
Absence makes the heart grow fonder. Imagine how much he'll get out of FB, if he has to wait three hours between starting work and break time.