As written previously on the Google SEO factors list, there is a “correlation but no causal relationship” between the number of likes, followers, social shares and rankings in the search engines.
Matt Cutts (which after 16 years has just left Google in order to work for the Pentagon..) categorically states that the Google algorithm does not take into account the social signals.
The misconception here is: is it reasonable to think that the same content, if quality, will have a similar rate of CTR on the different platforms. Consequently, there is a correlation relationship between positioning and spreading since the algorithms take (also) into account of the same metric.
Google will reward with improved positioning the results lower in the SERPs with best CTR, assuming that content to be more relevant for the specific search keywords.
Facebook will increase the coverage of the post, making it visible to a larger number of users
Since has adopted the new algorithm for displaying the feed (February 2016), Twitter, like Facebook, will increase the coverage of the post.