Look again Mike.
According to the NRA-ILA site, SD recognizes MN but not the other way around. Heck, SD recognizes my MA permit too!
I'll have to check into it. They used to, but I know in February they did not. Maybe we are lucky and they brought it back.
The original reason they dropped the reciprocity was because Minnesota wouldn't recognize theirs due to lower levels of training in SD, so SD responded with a dropping of MN. When I talked to my gunsmith he verified it. He also stated that that was the nice thing about an FFL - if he can show business related it becomes nationwide (not as simple as just nationwide, but close enough he can meet the requirements when he travels).