Easy solution: just do nothing. Compiler does it for you (as written in comments), as long as it's not an explicit ctor for AnotherClass:
class Child : public Parent
{
  public Child(std::string myString)
  : Parent(myString) {}
};
You can even consider simply using the ctor of Parent (by simply writing using Parent::Parent), albeit that changes the interface.
If you'd like to be verbose, you might say (again, as in the comments):
class Child : public Parent
{
  public Child(std::string myString)
  : Parent(AnotherClass(myString)) {}
};
These are for simple cases. However, sometimes you need to solve a more complicated issue before calling Parent's ctor: e.g., you'd like to reuse AnotherClass or do some calculation/verification on it. This is why I wrote the answer: in the generic case, you might need to do some arbitrary complex calculation. You might still do that, with the help of lambdas (or static member functions, or even free functions):
class Child : public Parent
{
  public Child(std::string myString)
  : Parent([&](){
    // here you can write any code
    // it'll run _before_ Parent's ctor
    AnotherClass ac(myString);
    // do any calculation on ac, store it, etc.
    return ac;
  }()) {}
};
Also, suggest using std::move when you pass the argument (unless, of course, when you need it in another place in the ctor as well).