It makes practical sense that DOJ cannot imprison the president because president is the boss of everyone working in and under DOJ. So s/he could (and probably

It makes practical sense that DOJ cannot imprison the president because president is the boss of everyone working in and under DOJ. So s/he could (and probably would) simply give them the order not to lock him or her up. But after s/he is out of the office I see no reason why s/he could not be imprisoned by the next president for the crimes committed while in office.