Can he propose to a woman whom his friend saw before and decided not to marry?

If this woman is of good character and is religiously committed, there is nothing wrong with proposing marriage to her. Women may be seen by more than one suitor before they get married to one of them. The mere fact that your friend looked at her does not mean that you cannot marry her. Even if she was married before, then she was divorced or her husband died, which is more serious than looking, would anyone hesitate to say that it is permissible to marry her? 

There are clear saheeh texts which speak of the matter about which you are asking, such as the following: 

It was narrated that Ibn ‘Umar (may Allaah be pleased with him) said: The Prophet (peace and blessings of Allaah be upon him) forbade outbidding one another, and no man should propose to a woman to whom his brother has already proposed, unless the first suitor gives up the idea or gives him permission to propose. 

Narrated by al-Bukhaari, 4848; Muslim, 1412 

This hadeeth shows that it is haraam to propose to a woman to whom someone else has already proposed, and that it is not permissible for the second suitor to propose unless the first suitor withdraws his proposal or gives permission to the second. This is what has happened with you and your friend. 

If you are sure that she is of good character and religiously committed, then you should pray istikhaarah, then propose to her. 

We ask Allaah to help you to do that which is best for you.  

And Allaah knows best.