As the heading says,
Is there a simple plugin or API to pull reviews from my facebook page?
Let me know if the below link helps. It is an activity feed which you can put on your website for the activity on your page. It gives you code to embed.
I don't know if there is a way to automatically pull just reviews from one site to another; as far as I know, you get everything or nothing. Or perhaps you have a section of your facebook page specifically for testimonials, in which case you could restrict the content of that feed to just that section. But even so, would you really want to?
It would be best to moderate the reviews before having them show up elsewhere; in most cases, two or three representative testimonials suffice, and are easy enough to copy and paste over manually. More than that and a site starts to lose its credibility.
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