I have a doubt concerning declaring variables, their scope, and if their address could be sent to other functions even if they are declared on the stack?

class A{
    AA a;
    void f1(){
        B b;
        aa.f2(&b);
    }
};

class AA{
B* mb;
f2(B* b){
mb = b;
//...
}
};

Afterwards, I use my AA::mb pointer in the code. So things I would like to know are following.
When the program exits A::f1() function, b variable since declared as a local variable and placed on the stack, can't be used anymore afterwards.

1. What happens with the validity of the AA::mb pointer?
   It contains the address of the local variable which could not be available anymore, so the pointer isn't valid anymore?
2. If B class is a std::<vector>, and AA::mb is not a pointer anymore to that vector, but a vector collection itself for example. I would like to avoid copying all of it's contents in AA::f2() to a member AA::mb in line mb = b. Which solution would you recommend since I can't assign a pointer to it, because it'll be destroyed when the program exits AA::f2()