Overloading "*" operator for a class to return class variable

I have two cpp files and one hpp file. Main.cpp, Ab.cpp and Ab.hpp.

In these files I have created a class 'Ab' that has a default constructor and a constructor that takes a string. Within the class I want to redefine the * operator to set a given value to an object of the class and also delete any previous value that was assigned to it.

It is with mentioning that I have been instructed that I am not allowed to use any copy constructor or copy assignemnt in this task. Meaning I have to resort to using purely move constructor and move assignemnt. And in these subjects my knowledge is very limited as I've only worked with basic C# before.

The Main.cpp is as following:

#include <iostream>
#include "Ab.hpp"

A MoveTest(std::string testData)
{
    return Ab(new std::string(testData));
}

int main()
{
    std::cout << "-----'Ab' Test Begin-----" << std::endl;


    std::cout << "'Ab' test: Constructor begins." << std::endl;
    Ab emptyAb;
    Ab moveTestAb(new std::string("To remove"));
    std::cout << "'Ab' test: Constructor done. Press enter to continue." << std::endl;
    std::cin.get();

    std::cout << "Ab' test: Moveoperator begins." << std::endl;
    moveTestAb = MoveTest("This is a test movement");
    std::cout << "Expected output:         " << "This is a test movement" << std::endl;
    std::cout << "Output from moveTestAb: " << *moveTestAb << std::endl;
    std::cout << "'Ab' test: Moveoperator done. Press enter to continue." << std::endl;
    std::cin.get();
    std::cout << "-----'Ab' Test End-----" << std::endl;
    std::cin.get();
}

The Ab.cpp is as following:

#include "Ab.hpp"

std::string Ab::Get() const
{
    return "test";
}
bool Ab::Check() const
{
    bool return_value = true;
    if (this==NULL)
    {
        return_value = false;
    }
    return return_value;
}

Ab & Ab::operator=(const Ab &ptr)
{
    return *this;
}


Ab & Ab::operator*(Ab &other)
{
    if (this != &other) {
        delete this->a_string;
        this->a_string = other.a_string;
        other.a_string = nullptr;
    }
    Ab *thing_to_return = &Ab(this->a_string);
    return *thing_to_return;  
}

The Ab.hpp is as following

#include <string>
class Ab
{
    Ab(const Ab&) = delete;

    std::string* a_string;
    public:
        Ab &operator=(const Ab&);

    Ab& operator*(Ab&);



        Ab();
        Ab(std::string *the_string):
        a_string(the_string){};
        int b = 0;
        int a = 3;
        std::string Get() const;
        ~Ab() = default;
        bool Check() const;

    private:
        int z = 0;
};

I am currently getting the error:

no operator "*" matches these operands -- operand types are: * AB