Is there a research on correlation between honesty and success? Did anyone do a research on corelation between honesty and success, establishing individual's honesty through a provocative experiment and comparing it with his/her salary amount, satisfaction of achievement etc?
Or anything close to that?
No provocative experiment needed. Some of the major taxonomies within personality psychology have well-validated measures for honesty, and have been used in massive samples that could already address this question. I would start by doing a search on Google Scholar for those measures and the types of success you mention. E.g.,


  https://en.wikipedia.org/wiki/Honesty-humility_factor_of_the_HEXACO_model_of_personality


Notice that the trait most often associated with success is Conscientiousness, which may include an aspect of honesty:


  https://en.wikipedia.org/wiki/Conscientiousness