I am puerto rican. My half sister is puerto rican and her mother was
black. She states that ALL puerto ricans have black blood in them. I
do not agree with that. I need to be able to prove to her that ALL
puerto ricans do not have black blood in them. She is a teacher so you
have to prove things in black and white to her. Can you help?

If you go back far enough, all of us may have origins in Africa:

"In recent years, researchers have traced all human beings to a common
female ancestress, an original Eve, who lived approximately 200,000
years ago in Africa. One of the implications of these findings is that
all human beings originated in Africa and the essential, 'natural'
human race is one, mutating into different groups over time due to
geographical migration."

http://globalexpress.initiativesofchange.org/issue16/lawrence.html

I have learned that it is extremely difficult to prove anything to a
person whose opinion is already set in stone. It sounds as if your
half sister has closed her mind on the issue. What kind of evidence
would she accept? That there are persons in Puerto Rico whose
ancestors all came from Europe? That would not be proof that they were
100% Caucasian, since many racial blends exist in Europe.

Personally, I do not believe it is possible to prove racial "purity,"
and if it were possible, I don't see what earthly difference it would
make.

Many biologists do not see race as a valid biological concept. The
argument is as follows:

There is more genetic similarity between the average person of race A
and the average person of race B than there is between any two
randomly selected members of race A. More simply put there is just as
much variation between blackk people or white people than there is
between the two groups.

With this in mind it might make sense to ask, are there any Puerto
Ricans who do not have any ancestors who originated in africa in the
past x years.

I don't know how to finf the answer to that question.