A/C problems or battery problems

What is your question?

2015 F350 Super Duty, A/C stopped working, waited to take it to the shop, drive it for about 700 miles without A/C then parked it at the park and ride at the airport. 30 days later I returned and the batteries were totally dead. Removed the batteries and got two new ones. Vehicle started right up fine. Funny thing is that the A/C started working and has been working ever since. Why is it that after replacing the batteries that the A/C started working?