Here is a link that discusses the requirements state by state. North Carolina will allow the use of an out of state learner's permit in most cases, South Carolina will not.
One issue is that different states have different restrictions. For instance, some states, including Virginia, will allow learners' permits for age 15; most states require age 16, and those states (e.g. North Carolina) won't honor a 15 year old's learners permit if that's the case for your son; he has to be 16. To one of the comments above, New York State will honor learner's permits only for people over the age of 18. People aged 16-17 from other states are not allowed to drive in certain parts of New York state even with a license, and in other parts of the state only with severe restrictions.
Also, states have different minimum age requirements for the (licensed) driver in the passenger's seat, typically 20 or 21. Finally, different states have rules/restrictions on class of cars, vehicles etc.
States have "rules" for learner's permits, but they are not "reciprocal."