itertools.tee wrongly programmed

The crux of the tee() function of itertools is that in duplicates/multiplies the generator so that you have independent generator copies: If one is depleated (StopIteration Exception) the others still are able to generate the sequence.

MPs itertools tee definition:

def tee(iterable, n=2):
    return [iter(iterable)] * n

does not achieve this.
My very first example from the book "Clean Code in Python" by Mariano Anaya using tee thus lead to an error.

Circuitpythons itertools practically has the same definition. -> same problem.

tee in CPython has to store the objects that some, but not all of the generator copies have produced. It is coded in C.
I see no other way to replicate this behaviour than to grow a list of those values. A deque with the option to retrieve intermediate objects would be optimal, which we do not have?!

Start by reading the itertools tee() definition shown in the issue and compare its behavior with CPython's tee implementation. Reproduce the case where one iterator is exhausted before the others; done means the returned iterators remain independent and can continue producing the sequence.