Fairness for High-Skilled Immigrants Act of 2019 This bill increases the per-country cap on family-based immigrant visas from 7% of the total number of such visas available that year to 15%, and eliminates the 7% cap for employment-based immigrant visas. It also removes an offset that reduced the number of visas for individuals from China. The bill also establishes transition rules for employment-based visas from FY2020-FY2022, by reserving a percentage of EB-2 (workers with advanced degrees or exceptional ability) and EB-3 (skilled and other workers) visas for individuals not from the two countries with the largest number of recipients of such visas. Of the unreserved visas, not more than 85% shall be allotted to immigrants from any single country.