Efficient way to construct object with string member

Suppose I have a class ThisHasAStringMember. Assume it has a private member which is a string, and I want to efficiently get the string value, preferring a move over a copy where possible. Would the following two constructors accomplish that?

class ThisHasAStringMember
{
public:
  // ctors
  ThisHasAStringMember(const std::string str) : m_str(str) {}
  ThisHasAStringMember(std::string &&str) : m_str(std::move(str)) {}

  // getter (no setter)
  std::string value() { return m_str; }
private:
  std::string m_str;
}

Do I need the double ampersand before the str parameter in the second constructor?

Is this the right way to accomplish this?