Sync WordPress blog and Facebook page

Hello all,

I installed the Facebook plugin but when I post a comment on the blog, on the same article on my fan page, there is nothing. Can we sync both?

Example:

Blog: https://www.letmebe.eu
Fan page: https://www.facebook.com/pages/Let-me-be/112207015516767

https://www.ads-software.com/extend/plugins/facebook/