How can Mjolnir Hammer joins the Far Eastern Magic Nap Society of Summer?
Based on Wikipedia,
The school is escalator school in anime version only.
Dekomori is anime only character that problem is not exist LN version.. 

Club system in escalator school is depends on the school.

Some schools have totally separate clubs.
Some schools have shared one club between junior high and high.
Some other school have joint club for cultural club and separate club for sports related club.

I'll try to add some reference about clubs in escalator school. (sorry links are in Japanese.)


From answer of this question(Does escalator school have shared club?), most school share the club between junior high and high. (The answer said they also have shared "seitokai" Student council)
Son of this blog author "graduated" baseball club in junior high, and joined high school club next day. so in this case clubs are separated.
This article said one of good thing of escalator school is share the club.