Section 9 of the U.S. Constitution, makes it illegal to accept any sort of pay, gift, favor, money, etc., from a foreign government, and hold any office in the US government. The reason is obvious - it shows fake allegiance to the US, and it is bribery. Both lack of allegiance and bribery, will disqualify anyone from becoming President.
Matters become EVEN WORSE for Hillary, when one applies the original ratified thirteenth amendment to the Connstitution, which further strengthens Section 9. This repeals citizenship altogether, for anyone who has accepted such gifts etc.. There is no dispute, that Hillary Clinton is exactly in such a position.
There is no way she can be legally recognized as a president of the United States.