Trump is just President-Elect, still just a citizen so they could charge or sue him but it would not stop the process as far as I know, however, this could influence the Electoral College. In December (I can't remember the day), they can change their votes and dump Trump, in this case it would be simple since Clinton won the popular vote. Irony huh, the Populist who glorified the virtues of the popular vote and denounced the Electoral College gets elected by the thing he calls anti-democratic process.
Another popular question of conflict of interest, as we have seen in the Fords, this is a good article:
Blind Trusts – Who Controls Donald Trump's Assets While President? - Hull & Hull LLP