I think they stay. One of my accounts changed group and i still had my group summons pack( I hadn't opened it). Unlike the group contributions, these things stay in your backpack which hold all items. When you need coins you exchange them. Once exchanged they become part of the group summons thing that is fed to the serpent to improve its chakra level. Until you exchange for 100000 coin a set, they still are part of your backpack and you can carry it to next group.

Someone verify this. I think this is right, if i understand the question right.