An issue on permissions of admin profile (admin and public admin)

I need that for "registered user" from public area to confirm registration and after it work on user. Not always possible:

In case I work as "Super admin" --> all is ok
In case I work as "Public admin" --> I cannot confirm registration
In case I work as "admin" --> I can confirm registration, but after it I lost user (I cannot manage him till admin assign to me)

So, there is a configuration way in order I can with a "Public admin" or "simple admin" (not super admin) to:
 a) confirm registration
 b) immediately have got available user for course assignment and managemetn

???
thank you in advance...