West Africans are not the largest immigrant group to migrate to the United States, but they are becoming more numerous in recent years. As the countries in this region are extremely diverse, it would be tricky to generalize about whether or not most immigrants achieved their goals. However, we can look at the evidence available and make some assumptions.
It seems that West African immigrants from certain nations, Nigeria and Ghana in particular, enjoy relatively beneficial situations in the United States. Many of them hold higher degrees and are also home English speakers, which gives them an advantage in the job market. They are more likely to be employed in higher-level positions, such as management, business, science, and the arts.
A little more than half of Sub-Saharan immigrants become naturalized US citizens, and many more become permanent residents, especially if they have family already living in the United States. For immigrants who retain strong ties to their home communities, the United States can provide employment opportunities that help them send money back to their place of origin. This is known as remittances, and according to the chart in Sub-Saharan African Immigrants (migrationpolicy.org), you can see that the number of remittances has risen significantly ever since 2004. This indicates that people are earning enough money in the US to send plenty of it back home.
In addition, some West African immigrants seek the United States because they feel unsafe in their country of origin. That is the case in the Reuters.com article, focusing on a woman from Cameroon. Her goal, quite simply, is to escape a dangerous situation and find asylum in the USA.