How can I use Unique_ptrs with an class object having std::function as argument in the constructor

auto bPtr = std::unique_ptr<B>(new B( std::function< std::unique_ptr<A>() > () ));
//                                     need to close the template         ^
//                                     need to construct an instance of     ^^

You get the same a bit simpler by using std::make_unique:

auto bPtr = std::make_unique<B>( std::function< std::unique_ptr<A>() >() );
//                                               still as above      ^^^

Edit: Adjustment to new question version:

You have not yet provided a copy constructor – so you need to store the lambda instead of creating a B instance:

auto l = []() { return std::make_unique<A>(); };
auto bPtr = std::unique_ptr<B>(new B(l));
// or:
auto ptr  = std::make_unique<B>(l);

Note that this new edited version provides a factory function to the std::function object (the lambda!), while the initial variants constructed an empty one without function stored inside, so not callable!

You might construct a B by passing a std::function (or value which might convert to).

For example appropriate lambda:

B b{[]() { return std::make_unique<A>(); }};

If you really want std::unique_ptr<B>, then it becomes:

std::unique_ptr<B> b = std::make_unique<B>([]() { return std::make_unique<A>(); });